This research studies the influence of constant pressure acting on the magnetic particles brush for the precision machining of planar and curved workpieces. In particular, it examined the effects of constant pressure on improving the formal accuracy of the workpiece. This process method, constant pressure is applied to the magnetic pole of a conventional magnetic brush, the constant pressure acted to the surface of the workpiece through the magnetic particle brush formed at the magnetic pole surface. The authors conducted a plane magnetic abrasive finishing experiment using both the conventional magnetic abrasive finishing process and the newly proposed constant-pressure magnetic abrasive finishing process to compare the deburring characteristics between the processes for removing burrs from holes drilled in brass plate workpieces. In this experiment, a brass disk with a drilled hole was used as a workpiece. As a result, the difference in finishing characteristics was clarified. The results showed that the burr can be removed by use of this new plane magnetic abrasive finishing process and it is more useful than the conventional magnetic brush for improving the shape accuracy of the workpiece.