Quantum communication is a frontier hotspot of current research, and it has ideal information security. In order to enable quantum systems in arid and desertified areas to work almost under all-weather condition, it is necessary to study the attenuation of free-space quantum signal transmission and the influence of the turbulence atmosphere carrying sand and dust on communication performance. Using Mie scattering theory, multiple scattering simulation method, and atmospheric turbulence theory, the attenuation of optical wave transmission in sand and dust turbulent atmospheric channels with different visibility, and the influence of multiple scattering and turbulence on attenuation are studied. The results show that the effect of multiple scattering increases with the decrease of visibility, the turbulence effect gradually strengthens with the increase of distance. According to the quantum amplitude damped channel model, the effects of multiple scattering and turbulence in the sand and dust turbulent atmosphere with different visibility on the quantum channel capacity, fidelity and bit error rate are analyzed. The results show that as the visibility decreases, the multiple scattering effect increases, resulting in the decrease of attenuation and bit error rate, but an increase in channel capacity, fidelity and the boundaries of security key rate. The existence of turbulence in the dust atmosphere will increase the attenuation and bit error rate, but reduce the channel capacity, fidelity and security key rate. It can be seen that the influence of multiple scattering and turbulence on the communication performance, when the visibility of the sand and dust atmosphere are both low, cannot be ignored. In practical applications, the relevant parameters of quantum communication should be adaptively adjusted according to the visibility and turbulence intensity to improve the probability, efficiency and reliability of quantum communication.