The downlink single input multiple output (SIMO) and uplink multiple input single output (MISO) technologies of laser communication of unmanned aerial vehicle (UAV) air-ground slant in atmospheric turbulence channel were studied. Based on the atmospheric turbulence model of Gamma-Gamma distribution, the Meijer function was used to derive the bit error rate (BER) closed expression of SIMO technology in downlink under the combined influence of atmospheric turbulence and pointing error. An approximate expression of BER performance of MISO technology in uplink of Gamma-Gamma turbulence model was established based on $\alpha -\mu$ distribution. The effects of antenna number, zenith angle and pointing error on the system were studied systematically. The results show that the spatial diversity technology can effectively improve the BER performance of the system. When the beam divergence angle is 500 μrad, and the downlink receiver as well as the uplink transmitter are 3, the performance optimization can be over 10 dB. The zenith angle has a significant influence on the BER performance of air-ground slant laser communication. In order to meet the performance requirement of 10^-6 of system BER, the zenith angle should be controlled within a small range of about 30 degrees.