Avoiding or tracking aerial targets for UAVs (unmanned aerial vehicles) can be regarded as a nonlinear motion guidance and control problem. In such kind of tasks, both of UAVs and targets have high maneuverability and time sensitivity. According to these characteristics, a motion guidance method in fine time based on Lyapunov stability theory was proposed. A framework for solving the two problems was constructed, then collision avoidance and maneuvering target tracking problem were transformed into reaching virtual target and rendezvous problem respectively. The problem of collision avoidance of UAVs was converted into the control problem of realizing parallel navigation, and then the guidance law was designed using the Lyapunov stability theory. For the problem of tracking maneuvering target, the guidance law was designed according the requirement of rendezvous based on former guidance law. The simulated experiments in a Gazebo platform were conducted, and results showed that the proposed method can effectively avoid larger maneuver overload for UAVs, thus having better adaptability for time-varying and parameters.