The present study is aimed to analyze the effect of process parameters on the qualities of the Friction Stir Welded AZ31B Mg Alloy. Response Surface Methodology based Grey Relation Analysis technique was used to multi-optimization of the response parameters such as tensile strength (TS), percentage elongation (El), microhardness (MH), and impact strength (IMP). The mathematical models for response parameters were developed by considering tool rotational speed (RS), tool shoulder diameter (SD), and welding speed (WS) as process parameters. ANOVA (Analysis of Variance) was performed to check the adequacy of the formulated mathematical model and figure out the significant parameters. The results revealed that RS of 950 rpm, WS of 150 mm/min, and SD of 11 mm are the optimal process parameters for optimum response parameters (TS of 157.8700 MPa, IMP of 4.3001 Joule, MH of 84.1335 Hv, and El of 10.0071%). WS is the most significant factor, followed by RS and SD. The grain growth was observed in thermo-mechanically affected zone (TMAZ). The fracture analysis indicated that crack had initiated from the bottom of the centerline in the welded zone and propagated towards the advancing side.