As an effective means to suppress harmonic pollution, boost PFC converter is widely used to solve the increasingly serious harmonic pollution problem in power grid. However, the input voltage of the PFC converter fluctuates sinusoidally with time. Therefore, different from the DC–DC converter with switching cycle equilibrium point, the PFC system cannot be directly evaluated by Lyapunov's indirect method. In this paper, the discrete-time mapping modeling method based on phase-by-phase angle analysis is used to establish the model of the boost PFC cascaded buck converter system and to solve the problem of time-varying system state equation and control equation, the period-doubling bifurcation and chaotic behavior of the system are analyzed, and the model error is analyzed. Finally, the simulation model is built, and the correctness of the theoretical analysis is verified by simulation.