On the basis of ordinary plane magnetic abrasive finishing, a finishing method is proposed that can improve the flatness of a plane workpiece. In this method, the feed speed is varied during finishing according to the profile curve of the initial surface and the material removal efficiency, to control the effective finishing time in different areas and thereby improve the surface flatness. A small magnetic pole with an end face diameter of 1 mm is designed, and a ferromagnetic plate is placed under the workpiece to improve the uniformity of the magnetic field distribution near the magnetic pole. An experiment on an A5052 aluminum alloy plate workpiece shows that after 60 min of finishing using the proposed method, the extreme difference of the workpiece surface can be reduced from 14.317 mu m to 2.18 mu m, and the standard deviation can be reduced from 3.322 mu m to 0.417 mu m. At the same time, according to the measurement results, a similar flatness can be achieved at different positions on the finishing area. Thus, the proposed variable-speed finishing method leads to obvious improvements in flatness. (C) 2021 Author(s).