The investigation of supersonic channel flow with periodic oscillatory backpressures at the outlet of the channel was performed using large-eddy simulation for the inlet free-stream Mach number 4 and the Reynolds number approximately $5.2 \times {10^4}$ based on the height of the channel. Results have been validated carefully against our experimental data. Three typical backpressures are considered for constant backpressure and both periodic oscillatory backpressures with low and high frequency. The oscillatory backpressure can obviously influence the flow features occurring up to the middle region of the channel for the low frequency case and the downstream region for the high frequency case. Obvious differences of phase-averaged quantities at different phases are observed for the low frequency backpressure while the differences are relatively small for the high frequency backpressure. The spectral analysis reveals that the flow field experiences a periodic-like evolution of flow structures including shocks and vortices for the low frequency backpressure, resulting in the enhancement of turbulence fluctuations due to the complicated interaction of shocks and vortices.