This paper presents a real-time path planning algorithm for UAVs to avoid collision with other aircraft. Reachable sets are used to represent the collection of possible trajectories of obstacle aircraft. It is used in collision prediction for UAVs in path planning. Once a collision is detected, a sampling-based method is used to generate a collision avoidance path. A second collision check is performed on the generated path with the updated UAV and aircraft' states. The path is re-planned if it leads to another collision. The algorithm is validated in Software-In-the-Loop simulation. ADS-B (Automatic Dependent Surveillance - Broadcast) data logged from commercial aircraft are used as the obstacle aircraft. The experiments show that reachable set improves the success rate for collision avoidance compared to the linear motion assumption for the obstacle aircraft.