This study develops a new surface polishing approach by combining planetary motion (PM) with two-dimensional vibration-assisted magnetic abrasive finishing (PM-2DVAMAF). Planetary motion involves both rotation and revolution, thus generating radial acceleration, which strengthens the normal force exerted on the workpiece surface, and in turn enhances the cutting power of the abrasives and their polishing performance. Assisted by two-dimensional vibration, PM results in uniform, intersecting, and closely packed polishing paths, which contribute to better surface quality within a shorter processing time. This study also uses the Taguchi experimental design method to obtain the optimal combination of PM-2DVAMAF parameters for surface roughness improvement. The optimal combination obtained includes working gap, 1 mm; amplitude of vibration, 0.1 mm; particle size of steel grit, 0.125 mm; weight of SiC, 3 g; weight of steel particles, 0.5 g; weight of machining fluid, 5 g; frequency of vibration along the X- and Y-directions, 16.67 Hz; and rotational speed of magnet, 500 rpm. Experimental results reveal that 12.5-min PM-2DVAMAF under optimal combination of parameters can reduce surface roughness of a stainless steel SUS304 workpiece from 0.14 to 0.032 μm, an improvement rate of 77.1 %. PM-2DVAMAF can indeed improve surface quality with a short machining time and less abrasives required, both of which contribute to cost reduction and more environmentally friendly machining method in industry.