An unmanned aerial vehicle (UAV) dynamic path planning method is proposed to avoid not only static threats but also mobile threats. The path of a UAV is planned or modified by the potential trajectory of the mobile threat, which is predicted by its current position, velocity, and direction angle, because the positions of the UAV and mobile threat are dynamically changing. In each UAV planning path, the UAV incurs some costs, including control costs to change the direction angle, route costs to bypass the threats, and threat costs to acquire some probability to be destroyed by threats. The model predictive control (MPC) algorithm is used to determine the optimal or sub-optimal path with minimum overall costs. The MPC algorithm is a rolling-optimization feedback algorithm. It is used to plan the UAV path in several steps online instead of one-time offline to avoid sudden and mobile threats dynamically. Lastly, solution implementation is described along with several simulation results that demonstrate the effectiveness of the proposed method.