Rendezvous is an important process of cooperative control for unmanned aerial vehicles (UAVs). Thus this paper investigates a cooperative path planning for rendezvous of UAVs with constant speed. To achieve both wandering maneuver with shorter range-to-go and circle maneuver with longer range-to-go, UAVs calculate the minimum maneuver distance to target in real time in order to plan a Dubins path as a reference. Based on this path, the UAV with shorter range-to-go re-plans the waiting maneuver to extend the path length. In addition, as the UAV with longer range-to-go also follows this manner, the UAVs will arrive at the boundary of the target execution range at the same time. To reduce the risk of collision in this range, the UAVs fly along the Dubins path to minimize the execution time. The simulation results show that the UAVs can perform cooperative path planning for rendezvous in target execution range by using the proposed method, and it is easy to implement the corresponding control law, which demonstrates the feasibility and effectiveness of the method.