Atmospheric turbulence is a mainly factor which restricts space laser communication. In this paper, a new turbulence simulation method was proposed. At the receiving position, a pair of correlated amplitude and phase screens was used to simulate the turbulent effects. For the situation of satellite to ground laser communication, firstly, the double infinite integral forms of the amplitude autocorrelation, phase autocorrelation and amplitude-phase cross-correlation functions were reduced to the forms of single integral; and then, according to these correlation functions, a pair of correlated amplitude and phase screens was simulated by using the covariance-based random screen simulation method. The conformities between the simulated structure functions and the theoretical ones were compared. The outer scale and inner scale of atmospheric can be considered in this simulation method.