Autonomous dynamic obstacle avoidance of unmanned aerial vehicles (UAVs) based on collision prediction is critical for stable flight missions. UAVs must deal with high‐speed and nonlinearly moving obstacles that obey nonlinear dynamics, which are one of the numerous objects affecting stable flight. To satisfy the requirements of smooth flight and attitude stability, a novel dynamic smooth obstacle avoidance (QVA) method based on obstacle trajectory prediction is proposed. To predict the dynamic obstacle trajectories, a trajectory prediction (QLTP) method using a quasi‐linear parameter varying representations is proposed. The proposed QVA integrates the QLTP approach, velocity obstacle (VO) approach, and artificial potential field (APF) methods. The QVA detects an imminent collision based on the QLTP method, and then replans the UAV path based on the VO method at the time of the predicted collision. The UAV tracks planned waypoints for collision avoidance. To ensure the flight safety of the UAV, a virtual APF is constructed with waypoints as local targets and obstacles. The simulation results show that the proposed method performs better than the improved APF and VO methods in terms of the smoothness of the obstacle avoidance path and the stability of the UAV attitude.