In order to generate electric power by thermoelectricity, thermoelectric modules are mounted on peripheral surface of a channel and hot fluid moves along the inside of the channel. Despite the importance of cross-section shape on the performance of power generator, no comprehensive study has been previously performed to clarify the thermal/hydraulic characteristics of different cross-sections on thermoelectric generators. Hence, in this paper, three-dimensional numerical simulations are carried out to investigate the performance of thermoelectric generators mounted on channels with five different cross-sectional shapes. The effect of Re number, hot air inlet temperature, thermoelectric cold side temperature, and load ratio on the maximum output power, pumping power, net power and thermal conversion efficiency are studied. Results revealed that the thermoelectric generator device with a rectangular-shape channel provides the highest output power and thermal conversion efficiency. With the increase of Re number, the amount of output power and pumping power increase. However, the net power and thermal conversion efficiency improves up to a specific Re number and then diminishes. Besides, increment of hot side inlet temperature intensifies the net power and thermal conversion efficiency of all channels while the increment of cold side temperature has a minor effect on the thermal conversion efficiency of thermoelectric.