To enhance the performance of thermoelectric generator (TEG) systems, a converging heat exchanger is proposed in this work, wherein the hot side wall is designed with an inward incline. Besides, a comprehensive fluid-thermal-electrical multiphysics model is established to predict the performance of the TEG system. The results indicate that the proposed model can be adopted to accurately assess the performance of the TEG system and that the temperature distribution should not be ignored in the numerical model. The gains provided by the converging structure increases with the increase of air temperature and the decrease of air mass flow rate. The design of the converging structure can also improve the voltage uniformity of the TEG system and reduce the backpressure power loss. According to a net power analysis, the optimal tilt angle is 2.5°, and the net power of the TEG system is increased by 20.2% at the temperature of 500 K and the mass flow rate of 30 g/s. Moreover, experimental data present a good agreement with model results. This work proposes a novel numerical method to accurately evaluate the performance of the TEG system and provides insight into the TEG design method regarding the tilt angle of the exhaust gas channel.