A new type of gas burner for Stirling engine that can recover adequate heat from exhaust gas was designed based on the plate heat exchanger and low-swirl combustion technology, which consists of three components: a cyclone, a burner, and a circular plate heat exchanger. The circular plate heat exchanger tightly wound around the combustion chamber plays a high efficiency of heat recovery role. In consideration of the radial symmetry of the burner, a three-dimensional numerical simulation was carried out by Ansys15. The velocity distribution, temperature distribution, and pressure distribution of the combustion gas were presented respectively. Strong backflow that came from the exhaust gas around the root of the flame in the combustion chamber and a vortex below the inlet of the exhaust gas channel were found, which were beneficial for the combustion and improving the uniformity of temperature distribution. Combustion behaviors of the burner under standard operating conditions were obtained, the highest temperature was about 2200 K in burner and the exhaust gas entered the plate heat exchanger at the temperature of 1375 K and exited at 464 K, with the waste heat recovery efficiency over 65.8%. And, the air-fuel ratio and combustion power had negligible effect on the waste heat recovery efficiency.