Based on the mechanism of magnetic abrasive finishing, the 7075 aluminum alloy (Al7075) was used in the experimental study. In order to improve wall surface quality and to remove the edge burrs of the hole, a novel magnetic abrasive finishing process was proposed. First, the radial magnetizing pole for the inner surface finishing process was confirmed. The evaluation of magnet spinning speed, abrasive mesh, and abrasive filling amount on the diameter deviation of the hole and surface roughness of the inner wall was studied. According to the characteristics of magnetic abrasive finishing process, Taguchi’s method was used to carry out the test. Through the analysis of variance, the best process parameters were determined and verified. The inner surface roughness was further decreased and the surface morphology was more uniform after finishing process. Second, the edge burr removal process of the hole exit was also studied, and the geometry of the burrs was measured before and after the magnetic abrasive finishing process. The results show that the burrs were significantly removed and the burr removal efficiency was improved by 33.3% compared with the conventional magnetic abrasive finishing process. Finally, the improved magnetic abrasive finishing process is an effective method in improving finishing quality of the Al7075 holes.