In this study, the combined thermodynamic and dynamic model of a new concept of gamma type free-piston Stirling engine is conducted. The engine consists of two identical displacer cylinders, a power cylinder, a linear alternator, and three-cushion pistons. Two displacer cylinders are symmetrically positioned on each side of the power cylinder for minimizing the rotational vibrations. Hydrogen is used as the working gas and the effect of gas temperature on the specific heat capacity is considered. The analysis carried out in this study involves the prediction of the thermodynamic-dynamic performance characteristics of the engine. In the thermodynamic section of the analysis, the working space of the engine is divided into 31 nodal volumes and the gas pressures in nodal volumes are assumed to be equal to each other. The conservation of mass and energy equations is obtained for each nodal volume. Instantaneous gas temperatures of nodal volumes are calculated by the first law of thermodynamics given for the unsteady open systems. The dynamic section of the analysis involves the motion equations of displacer, power and cushion pistons. The motion equations are derived using the Newton method. In the calculations done for variable specific heat capacity, it has been determined that there is 1% cyclic work reduction compared to the constant heat capacity. It is estimated that the maximum effective power that can be produced by the linear alternator will be around 1.6 kW. The working frequency range of the proposed engine is found to be suitable to generate electrical power.