Friction stir welding (FSW) can be made to improve the mechanical properties in the weld zone. This article aims to obtain the optimum FSW process parameters for two plates of AA5083 welded joints. The significant factors in the FSW process are tool rotational speed (TRS) and tool transverse speed (TTS), and the weld process conditions are Submerged FSW and Normal FSW. For doing the investigation, the Taguchi method L18 orthogonal array design of experimentation is utilized. Using the Grey Relational Analysis (GRA) to calculate the grey relation grade, the response parameters are tensile strength, microhardness, and surface roughness. The optimum process parameters have been recognized, and ANOVA controls the significant contribution of process parameters. The optimal FSW process parameters are used to maximize the FSW joint strength. It is identified in the condition of Submerged FSW, high tool rotational speed, and low TTS.