This paper introduces a quadrotor's autonomous take-off and landing system on a moving platform. The designed system addresses three challenging problems: fast pose estimation, restricted external localization, and effective obstacle avoidance. Specifically, first, we design a landing recognition and positioning system based on the AruCo marker to help the quadrotor quickly calculate the relative pose; second, we leverage a gradient-based local motion planner to generate collision-free reference trajectories rapidly for the quadrotor; third, we build an autonomous state machine that enables the quadrotor to complete its take-off, tracking and landing tasks in full autonomy; finally, we conduct experiments in simulated, real-world indoor and outdoor environments to verify the system's effectiveness and demonstrate its potential.