Free-piston engine generators (FPEGs) can be applied as decarbonized range extenders for electric vehicles because of their high thermal efficiency, low friction loss, and ultimate fuel flexibility. In this paper, a parameter-decoupling approach is proposed to model the design of an FPEG. The parameter-decoupling approach first divides the FPEG into three parts: a two-stroke engine, an integrated scavenging pump, and a linear permanent magnet synchronous machine (LPMSM). Then, each of these is designed according to predefined specifications and performance targets. Using this decoupling approach, a numerical model of the FPEG, including the three aforementioned parts, was developed. Empirical equations were adopted to design the engine and scavenging pump, while special considerations were applied for the LPMSM. A finite element model with a multi-objective genetic algorithm was adopted for its design. The finite element model results were fed back to the numerical model to update the LPMSM with increased fidelity. The designed FPEG produced 10.2 kW of electric power with an overall system efficiency of 38.5% in a stable manner. The model provides a solid foundation for the manufacturing of related FPEG prototypes.