The wireless laser communication technology using optical quantum detection has broad application prospects in heaven and earth integrated secure communication networks. Based on the Poisson distribution model of photon number of a laser source, the atmospheric turbulence Gamma-Gamma model, the response model of the single photon detector, and the correlation counting signal processing method, we establish a calculation model of bit error rate of the optical quantum communication system in the turbulent channel. The effects of the distribution of photon number of the laser source, turbulent channel parameter, performance parameters of single photon detectors, and correlation counting method on the system BER are simulated. The results show that the system BER is negatively correlated with the average photon number of laser pulses, pulse frequency, and detector detection efficiency, while it is positively correlated with atmospheric turbulence intensity and detector dark counting. The system adopting the correlation counting method can effectively reduce the system BER. When the number of door openings is determined, the system has an optimal threshold for discrimination. The proposed model can provide references for the design and optimization of the optical quantum communication systems.