The friction stir spot welding process has attracted joining of lightweight materials, which are generally difficult to weld conventionally. The strength of the friction stir spot-welded aluminum alloys will be affected by the process parameters, such as tool rotational speed, plunge rate, plunge depth, and dwell time. The response surface methodology was used to develop the empirical relationship to predict strength of the welded joints incorporating process parameters. It is found that the strength increases with the increase of tool rotational speed, plunge rate, and dwell time to a certain value and then decreases, but the initial increase of plunge depth increases the strength and further increase of plunge depth does not influence the joint strength. The developed empirical relationship was optimized by Hooke and Jeeves algorithm to attain maximum lap shear strength of the friction stir spot-welded AA7075 aluminum alloy joints. Sensitivity analysis was also carried out to understand the impact of each process parameters on lap shear strength of the joint.