In mobile communication, due to the Doppler shift in the receiver, the wireless signals encounter Doppler spectrum which results in the correlation in time domain. This sort of wireless signals usually are modeled as Rayleigh distributed signals and play a vital role in the researches for mobile communications. In this research we first use the inverse discrete Fourier transform (IDFT) technique to convert the Doppler spectrum into time domain and thus product the time domain Rayleigh fading signals. After that, we propose to establish the finite state Markov channel(FSMC) model based on the concept of average duration fade(ADF). Using this model, we may simulate the Rayleigh fading channels. We believe the simulation method may be used in the research for mobile communication.