Abstract: The free-piston Stirling engine serves as an efficient space power device that can form a novel power system when integrated with high-performance generators. This study investigated multiple dynamic parameters affecting the performance of a free-piston Stirling engine （FPSE）. Considering that FPSE performance is influenced by a combination of factors, an integrated approach combining orthogonal simulation design and grey relational analysis was employed to identify key parameters and improve engine performance. First, four main experimental factors were selected: displacer mass, power piston mass, displacer spring stiffness, and power piston spring stiffness. Four corresponding levels for each factor were determined based on engineering constraints, and a four-factor, four-level orthogonal experimental scheme was designed. Subsequently, the entropy weight method was applied to objectively assign weights to performance evaluation metrics, quantifying and assessing their respective influence on FPSE performance. At the same time, grey relational analysis was then conducted to comprehensively assess the performance of all 16 experimental combinations. The combination exhibiting the highest grey relational grade was identified as the optimal configuration. Further analysis involved calculating the average grey relational values for each factor across different levels to determine the theoretically optimal parameter configuration. Finally, a control group was selected based on the power piston mass to enable a more comprehensive evaluation of different parameter combinations. Through comparative analysis of performance indicators, it was found that when the displacer spring stiffness is 2.02×10⁴ N/m, the power piston spring stiffness is 8.0×10³ N/m, the displacer mass is 0.075 kg, and the power piston mass is 0.27 kg, the displacer and power piston amplitudes reach 2.98 mm and 6.261 mm, respectively, with a thermal efficiency of 35.39% and an output power of 90.97 W. This combination demonstrates superior performance among the three comparison schemes. These findings provide important guidance for engineering design and significantly enhance the overall performance of free-piston Stirling engines.