This study introduces a novel gas combustor structure designed specifically for a freepiston Stirling generator (FPSG) and presents a numerical simulation of the heat transfer characteristics of external combustion coupled with internal oscillating flow within the novel combustor-coupled FPSG system, fueled by liquefied petroleum gas (LPG). The simulation initially focuses on analyzing the flow field, temperature distribution, and heat flux density characteristics within the combustor under its rated operating conditions. Furthermore, the study investigates the effects of fuel flow rate, nozzle structure, and air preheating temperature on the flow dynamics and heat transfer characteristics. The results indicate that, at the rated operating condition with a fuel flow rate of 4.6 L/min and an air-fuel ratio of 29, the high-temperature heat exchanger (HHX) absorbs 3.82 kW of heat, which corresponds to 54.65% of the reaction heat, with comparable contributions from convective and radiative heat transfer. Interestingly, increasing the fuel flow rate and air-fuel ratio initially leads to a rise in the heat accepted, followed by a subsequent reduction. Moreover, the calculations demonstrate that raising the air preheating temperature significantly reduces the heat accepted under specific heat absorption conditions, while the impact of the nozzle structure remains negligible.