A new three-dimensional(3D) autonomous obstacle avoidance algorithm is proposed to solve the problem of obstacle avoidance during the flight of unmanned aerial vehicle(UAV). Firstly, the irregular obstacles are modeled by standard convex bodies according to some information of obstacles, and one or more standard convex bodies are used to cover the whole or key parts of the obstacle. Then, the arc obstacle avoidance trajectory strategy is designed according to the obstacle model, the obstacle avoidance problem is transformed into the avoidance trajectory tracking problem, and the rules of the decision and direction obstacle avoidance and the criterion of successful obstacle avoidance are defined. Finally, combined with the nonlinear guidance law and height channel control, UAV real-time three-dimensional trajectory tracking control and autonomous obstacle avoidance are realized. The nonlinear numerical simulation shows that the obstacle avoidance algorithm can effectively avoid obstacles and has high accuracy of 3D trajectory tracking, which can be applied to UAV obstacle avoidance missions.