The study performs a dynamic analysis of a micro-segment gear system with respect to the time-varying stiffness, gear backlash, time-varying pressure angle, and comprehensive error. The period expansion method is proposed to construct a single-degree-of-freedom nonlinear dynamic model of a spur micro-segment gear pair. In order to improve the accuracy of simulation results, the time-varying mesh stiffness and time-varying pressure angle is expressed in terms of a piecewise Fourier function. The effect of mesh frequency, backlash, mesh damping, and input power on bifurcation and chaos properties of the system are analyzed. The numerical results indicate that the system performs a chaotic motion after several frequency jumps as the mesh frequency increases. When the backlash increases, the frequency region of double sides impact and chaos tends to be decreased. The effect of mesh damping and input power on bifurcation characteristics is also investigated. The increase of mesh damping and input power can stabilize the system and avoid double sides impact. The results potentially present a useful source of reference for technicians and engineers for the dynamic design and vibration control of the aforementioned system with a non-constant pressure angle.