This study focused on the optimization of Al—Mg to CuZn34 friction stir lap welding (FSLW) process for optimal combination of rotational and traverse speeds in order to yield favorable fracture load using Grey relational analysis (GRA). First, the degree of freedom was calculated for the system. Then, the experiments based on the target values and number of considered levels, corresponding orthogonal array, Grey relational coefficient and Grey relational grade were performed. In the next step, Grey relational graph of each level was sketched. The performed graph and analysis of Grey results proved the impact of rotational speed and traverse speed on fracture load of resultant joints. Finally, the optimum amount of each parameter for better strength of the welds was obtained. This study showed feasibility of the application of Grey relational analysis for achieving dissimilar friction stir lap welds with the highest quality.