In order to study the effect of gas density on the terahertz wave radiated by multi-color laser-induced air plasma filament, a theoretical model of terahertz （THz） generation from a laser-induced air plasma filament and the subsequent propagation process is established. Based on the model and simulation, the influence of gas density on terahertz radiation is studied. The results show that the gas density will affect the transient current distribution of laser filament and the propagation phase of THz wave, then affect the THz radiation intensity of laser filament, and make the THz radiation energy change nonlinearly with the gas density. The theoretical study is of great significance to the cognition of the physical process of laser filamentation.