In order to study the influences of frictional coefficient on nonlinear dynamics of face-gear transmission system, a nonlinear dynamic model with multiple degrees of freedom is presented by the method of concentrated parameters. The model includes frictional, gear clearances, general transmission error, time-varying meshing stiffness, meshing damping, brace stiffness, support damping, exciting frequency, and external load, etc. The Runge-Kutta numerical integral method used to solve the dynamic differential equations. And the bifurcation characteristics were obtained under different rotation speeds and external loads. The calculation results show that the nonlinear dynamics characteristics of face-gear transmission system contain periodic response and chaotic response, and the amplitude is increased with the frictional coefficient increasing.