To address the problem that neighbor table of greedy geographical routing protocols can not accurately list positions of nodes, which resulted from periodic beacon exchange in unmanned aerial vehicle(UAV) ad hoc network. a mobility prediction greedy perimeter stateless routing protocol (MP-GPSR) is proposed. In the proposed protocol, the next hop is chosen according to the mobility location of neighbor nodes and link expiration time during the routing discovery phase, which slows down the adverse effect caused by the high speed moving of mode. Simultaneously choosing the next hop with the position information of the 2-hop neighbors when the routing void appears can reduce the redundancy of perimeter forwarding. Simulation result shows that the proposed protocol has high packet success delivery ratio and low average end-to-end delay as well as control consumption.