The UAV free space optical (FSO)/radio frequency (RF) hybrid relay-link transmission rate optimization method was proposed for the mismatch of communication rate between the FSO link and the RF link, and the problem of communication service state change caused by ground multi-user movement. Taking user fairness, minimum quality of service and total UAV power as constraints, a free space optical communication/radio frequency (FSO/RF) hybrid communication downlink model through UAV relay was established, and a joint optimization algorithm based on UAV dynamic trajectory and transmitting power was proposed. Using successive convex approximation and Lagrange dual function method, the original nonconvex model was transformed into a convex optimization problem for solving. Analysis of the link transmission rates at different visibility levels shows that both the FSO link and the RF link reach full-speed transmission when the visibility is 1.7 km. The proposed algorithm has a 447.5% improvement over fixed relay and a 32.5% improvement over non-power optimization algorithm link in average communication rate.