To study the joint effects of turbulence and fog on free-space optical (FSO) communication, a joint fog-turbulence-pointing error probability model for FSO is derived based on the random fog channel, Malaga turbulence model, and pointing error model. The closed-form expressions for the average signal to noise ratio (SNR), outage probability, average bit error rate (BER), ergodic channel capacity, and moment generating function in FSO communication under intensity modulation/direct detection are derived based on the joint model. Based on the unmanned aerial vehicle (UAV) working scenario, applying these expressions, the performance analysis of the inter-UAVs optical wave communication is implemented under the conditions for different beam widths, turbulence intensity and fog density and the pointing error caused by position, orientation, and jitter deviations. The calculated results are in good agreement with the Monte Carlo simulations. The analytical results for the average BER and outage probability show that the increase in beam width can significantly degrade the BER and outage probability, for the UAVs optical communication link. The analysis for the ergodic channel capacity shows that it increases with the increase of average transmission power; however, it increases slowly with the increase of beam width. And the increase in turbulence intensity, fog density, and drone jitter will degrade the communication performance of the system. Our study lays an important theoretical foundation for the development of FSO communication and UAV communication performance improvement in joint fog and turbulent environment.