Abstract A magnetic abrasive finishing is a non-traditional technology utilizes a flexible magnetic abrasive brush comprises of magnetic abrasive particles under the influence of the magnetic field to perform nano-finishing. The material removal (MR) and percentage change in surface roughness (%∆R a ) are responses governing the efficiency of the finishing process. But, a high material removal during the finishing operation leads to the loss in form/shape of the finished surface. A compromise has to be made considering the two responses for an optimized finishing operation. In this work, a multi-response optimization was executed using grey relation analysis (GRA). The objective functions considered are to maximize %∆R a and minimize MR. The experiments were designed and conducted using response surface methodology. The workpiece material was taken as AZ-31 alloy. The optimized conditions observed were %∆R a as 67.43% and MR as 63 mg at the working gap of 2 mm, rotational speed of 600 rpm, voltage of 18 volts and abrasive particle mesh number of 400 mesh. The GRA also reveals that the working gap has the strongest influence on the finishing considering both responses concurrently. The ANOVA analysis was also executed to analyze the significant interaction effects of process parameters on output responses.