In this paper, a dynamic two-stage closed search (DTSCS) scheme for the unmanned aerial vehicle (UAV) cooperative region search is designed, which satisfies the range constraint (RC) and orientation constraint (OC). The closed trajectory is composed of two coupling stages, the search stage and the return stage. The position and orientation at the end of the search stage are the starting cell and orientation of the return stage. In the first stage, a coevolution pigeon-inspired optimization (CPIO) algorithm based on the cooperation-competition mechanism is proposed for multi-UAV cooperative search. In the return stage, inspired by region searching and trajectory tracking, a search tracking (ST) approach is presented to obtain the lowest-cost path under OC. The simulation results show that: (i) N p = 5 is the best prediction time step. (ii) CPIO algorithm performs better than the compared intelligent algorithms in region searching. (iii) ST has high tracking performance than other algorithms. (iv) The DTSCS scheme enables every UAV to make the best use of its fuel to cover more region and return to the airport within the RC, and the average range utilization of UAVs is 97% under the 3OC.