Filed Pursuant to Rule 424(b)(3)
Registration File No.: 333-262607

BLACKROCK CORE BOND TRUST

Supplement dated May 10, 2023 to the

Prospectus and Statement of Additional Information (“SAI”),

each dated February 9, 2022, as supplemented on July 18, 2022

This supplement amends certain information in the Prospectus and SAI, each dated February 9, 2022, as supplemented on July 18, 2022, of Blackrock Core Bond Trust (the “Trust”). Unless otherwise indicated, all information included in the Prospectus and SAI that is not inconsistent with the information set forth in this supplement remains unchanged. Capitalized terms not otherwise defined in this supplement have the same meanings as in the Prospectus and SAI, as applicable.

Effective on or about May 31, 2023, the following changes are made to the Fund’s Prospectus and SAI:

The section of the Prospectus entitled “Management of the Trust — Portfolio Managers” is deleted in its entirety and replaced with the following:

Portfolio Managers

The members of the portfolio management team who are primarily responsible for the day-to-day management of the Trust’s portfolio are as follows:

Scott MacLellan, CFA, CMT, Managing Director, is a portfolio manager in BlackRock’s Global Fixed Income Group. He is the co-lead portfolio manager of BlackRock’s Low Duration Bond Fund, BGF USD Short Duration Bond Fund and the iShares Short Maturity Bond ETF (NEAR). As a lead portfolio manager on the USD short duration fixed income platform, he also focuses on managing a large number of multi sector fixed income separate accounts. Mr. MacLellan is also named as the sole lead portfolio manager for the BlackRock Target Allocation Shares Series P Fund. He is also the lead portfolio manager for four multi-sector BlackRock closed end funds, the BlackRock Core Bond Trust, BlackRock Multi-Sector Income Trust, BlackRock Limited Duration Income Trust and Enhanced Government Fund. During his career in multi-sector fixed income he also served on BlackRock’s Obsidian hedge fund team. Mr. MacLellan serves in number of capacities with regard to ESG investing in the Fundamental Fixed Income Team, including as a member of the Global Fixed Income ESG Leadership Committee and a member of the ESG Advisory Group to the Fundamental Fixed Income Executive Committee. Prior to assuming his current responsibilities in 2012, Mr. MacLellan was a an account manager in the Global Client Group, covering clients in Asia and the Middle East. He also served as a product specialist for short duration fixed income products. Previously, Mr. MacLellan spent four years with Nomura BlackRock Asset Management (NBAM), a former joint venture between BlackRock and Nomura Asset Management Co., Ltd, in Tokyo as an account manager. Prior to joining NBAM in 2001, Mr. MacLellan spent a year in the Global Finance and Investment Department of Industrial Bank of Japan Leasing in Tokyo investing in emerging markets. Mr. MacLellan earned a BA degree, with combined honors, in economics and international development studies from King’s College, Dalhousie University in Canada. Mr. MacLellan attended the Graduate School of International Relations and Pacific Studies at the University of California, San Diego and Tohoku University in Japan. He has received both the Chartered Financial Analyst and Chartered Market Technician designations. He is proficient in Japanese.

Akiva Dickstein, Managing Director, is Head of Customized Multi-Sector, US Short Duration, and co-Head of Global Inflation Linked Portfolios within BlackRock’s Global Fixed Income (GFI) group, and a member of the Global Fixed Income executive team. He is also a portfolio manager of BlackRock’s Core Bond and Short Duration Bond Funds. Prior to taking on his current responsibilities, Mr. Dickstein was the lead portfolio manager on BlackRock’s mortgage portfolios. Before joining BlackRock in 2009, Mr. Dickstein spent eight years at Merrill Lynch, where he served as Managing Director and head of the U.S. Rates & Structured Credit Research Group. He was responsible for the team that produced MBS, ABS, CMBS, Treasuries, swaps, and interest rate derivatives research. Mr. Dickstein’s publications on MBS strategy included the weekly Mortgage Investor as well as numerous lengthier articles on topics such as optimal loan modifications, the valuation of

credit-sensitive MBS and ABS, and the pricing of mortgage derivatives, options, and pass-throughs. In addition, he developed Merrill’s prepayment models for fixed rate and hybrid MBS. From 1993 to 2001, Mr. Dickstein was with Lehman Brothers, most recently as a Senior Vice President in Mortgage Derivatives Trading. In this role, he traded mortgage derivatives and developed Lehman’s credit default model. He joined Lehman as a mortgage and asset-backed securities analyst and was named to Institutional Investor’s All American Fixed Income Research Team in pass-throughs, non-agency mortgages, and asset-backed securities. Mr. Dickstein earned a BA degree in economics, summa cum laude, from Yale University in 1990, and an MA degree in physics from Princeton University in 1993.

The SAI provides additional information about each portfolio manager’s compensation, other accounts managed by the portfolio management team and the ownership of the Trust’s securities by each portfolio manager.

The section of the SAI entitled “Management of the Trust — Portfolio Management” is deleted in its entirety and replaced with the following:

Portfolio Management

Portfolio Manager Assets Under Management

The following table sets forth information about funds and accounts other than the Trust for which the portfolio managers are primarily responsible for the day-to-day portfolio management as of December 31, 2021:

Portfolio Manager Compensation Overview

The discussion below describes the portfolio managers’ compensation as of December 31, 2021.

The Advisor’s financial arrangements with its portfolio managers, its competitive compensation and its career path emphasis at all levels reflect the value senior management places on key resources. Compensation may include a variety of components and may vary from year to year based on a number of factors. The principal components of compensation include a base salary, a performance-based discretionary bonus, participation in various benefits programs and one or more of the incentive compensation programs established by the Advisor.

Base Compensation. Generally, portfolio managers receive base compensation based on their position with the firm.

Discretionary Incentive Compensation. Discretionary incentive compensation is a function of several components: the performance of BlackRock, Inc., the performance of the portfolio manager’s group within BlackRock, the investment performance, including risk-adjusted returns, of the firm’s assets under management or supervision by that portfolio manager relative to predetermined benchmarks, and the individual’s performance and contribution to the overall performance of these portfolios and BlackRock. In most cases, these benchmarks

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are the same as the benchmark or benchmarks against which the performance of the Trust or other accounts managed by the portfolio managers are measured. Among other things, BlackRock’s Chief Investment Officers make a subjective determination with respect to each portfolio manager’s compensation based on the performance of the Trust and other accounts managed by each portfolio manager relative to the various benchmarks. Performance of fixed income funds is measured on a pre-tax and/or after-tax basis over various time periods including 1-, 3- and 5- year periods, as applicable. With respect to these portfolio managers, such benchmarks for the Trust and other accounts are:

Distribution of Discretionary Incentive Compensation. Discretionary incentive compensation is distributed to portfolio managers in a combination of cash, deferred BlackRock, Inc. stock awards, and/or deferred cash awards that notionally track the return of certain BlackRock investment products.

Portfolio managers receive their annual discretionary incentive compensation in the form of cash. Portfolio managers whose total compensation is above a specified threshold also receive deferred BlackRock, Inc. stock awards annually as part of their discretionary incentive compensation. Paying a portion of discretionary incentive compensation in the form of deferred BlackRock, Inc. stock puts compensation earned by a portfolio manager for a given year “at risk” based on BlackRock’s ability to sustain and improve its performance over future periods. In some cases, additional deferred BlackRock, Inc. stock may be granted to certain key employees as part of a long-term incentive award to aid in retention, align interests with long-term shareholders and motivate performance. Deferred BlackRock, Inc. stock awards are generally granted in the form of BlackRock, Inc. restricted stock units that vest pursuant to the terms of the applicable plan and, once vested, settle in BlackRock, Inc. common stock. The portfolio managers of this Trust have deferred BlackRock, Inc. stock awards.

For certain portfolio managers, a portion of the discretionary incentive compensation is also distributed in the form of deferred cash awards that notionally track the returns of select BlackRock investment products they manage, which provides direct alignment of portfolio manager discretionary incentive compensation with investment product results. Deferred cash awards vest ratably over a number of years and, once vested, settle in the form of cash. Only portfolio managers who manage specified products and whose total compensation is above a specified threshold are eligible to participate in the deferred cash award program.

Other Compensation Benefits. In addition to base salary and discretionary incentive compensation, portfolio managers may be eligible to receive or participate in one or more of the following:

Incentive Savings Plans— BlackRock, Inc. has created a variety of incentive savings plans in which BlackRock, Inc. employees are eligible to participate, including a 401(k) plan, the BlackRock Retirement Savings Plan (RSP), and the BlackRock Employee Stock Purchase Plan (ESPP). The employer contribution components of the RSP include a company match equal to 50% of the first 8% of eligible pay contributed to the plan capped at $5,000 per year, and a company retirement contribution equal to 3-5% of eligible compensation up to the Internal Revenue Service limit ($290,000 for 2021). The RSP offers a range of investment options, including registered investment companies and collective investment funds managed by the firm. BlackRock, Inc. contributions follow the investment direction set by participants for their own contributions or, absent participant investment direction, are invested into a target date fund that corresponds to, or is closest to, the year in which the participant attains age 65. The ESPP allows for investment in BlackRock, Inc. common stock at a 5% discount on the fair

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market value of the stock on the purchase date. Annual participation in the ESPP is limited to the purchase of 1,000 shares of common stock or a dollar value of $25,000 based on its fair market value on the purchase date. All of the eligible portfolio managers are eligible to participate in these plans.

Securities Ownership of Portfolio Managers

As of December 31, 2021, the end of the Trust’s most recently completed fiscal year end, the dollar range of securities beneficially owned by each portfolio manager in the Trust is shown below:

Potential Material Conflicts of Interest

The Advisors have built a professional working environment, firm-wide compliance culture and compliance procedures and systems designed to protect against potential incentives that may favor one account over another. The Advisors have adopted policies and procedures that address the allocation of investment opportunities, execution of portfolio transactions, personal trading by employees and other potential conflicts of interest that are designed to ensure that all client accounts are treated equitably over time. Nevertheless, the Advisors furnish investment management and advisory services to numerous clients in addition to the Trust, and the Advisors may, consistent with applicable law, make investment recommendations to other clients or accounts (including accounts which are hedge funds or have performance or higher fees paid to the Advisors, or in which portfolio managers have a personal interest in the receipt of such fees), which may be the same as or different from those made to the Trust. In addition, BlackRock, Inc., its affiliates and significant shareholders and any officer, director, shareholder or employee may or may not have an interest in the securities whose purchase and sale the Advisors recommend to the Trust. BlackRock, Inc. or any of its affiliates or significant shareholders, or any officer, director, shareholder, employee or any member of their families may take different actions than those recommended to the Trust by the Advisors with respect to the same securities. Moreover, the Advisors may refrain from rendering any advice or services concerning securities of companies of which any of BlackRock, Inc.’s (or its affiliates’ or significant shareholders’) officers, directors or employees are directors or officers, or companies as to which BlackRock, Inc. or any of its affiliates or significant shareholders or the officers, directors and employees of any of them has any substantial economic interest or possesses material non-public information. Certain portfolio managers also may manage accounts whose investment strategies may at times be opposed to the strategy utilized for a fund. It should also be noted that Messrs. Dickstein and MacLellan may be managing hedge fund and/or long only accounts, or may be part of a team managing hedge fund and/or long only accounts, subject to incentive fees. Messrs. Dickstein and MacLellan may therefore be entitled to receive a portion of any incentive fees earned on such accounts.

As a fiduciary, the Advisors owes a duty of loyalty to its clients and must treat each client fairly. When the Advisors purchase or sell securities for more than one account, the trades must be allocated in a manner consistent with its fiduciary duties. The Advisors attempt to allocate investments in a fair and equitable manner among client accounts, with no account receiving preferential treatment. To this end, BlackRock, Inc. has adopted policies that are intended to ensure reasonable efficiency in client transactions and provide the Advisors with sufficient flexibility to allocate investments in a manner that is consistent with the particular investment discipline and client base, as appropriate.

Shareholders should retain this Supplement for future reference.

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