The performance analysis and optimization of a γ-type free-piston Stirling engine (FPSE) are conducted using Response Surface Methodology (RSM) and Grey Relation Analysis (GRA). The input-output parameters table is determined by the RSM. A regression model is presented to investigate the influence of structural parameters of FPSE on its performance. The relation coefficients for the four output parameters obtained from the RSM are determined to be 0.9980, 0.9983, 0.9999, and 0.9995, respectively, thus unequivocally demonstrating the exceptional precision of the RSM model. Also, the relationship between displacer and piston amplitudes, operating frequency, and output power and these parameters of Stirling engine is presented via 3D surface plots. The performance of the FPSE is optimized using the desirability approach and GRA, respectively, followed by a comparison of four groups of optimization results to determine the most suitable model. The maximum output power achieved is 78.02 W, with corresponding operating frequency, displacer amplitude, and piston amplitude values of 60.24 Hz, 2.55 mm, and 7.27 mm. Finally, by comparing pre- and post-optimization, the output power is increased by 36.85%. The GRA exhibits superior optimization compared to the RSM, thus providing valuable guidance for enhancing the optimization of FPSE in this study.