Abstract: Free flying target catching is a dynamic task. When this task is executed, in order to catch up with the free flying target in the minumun time, the quadrotor not only need to plan a time optimal trajectory to pursue the target, but also need to replan the trajectory based on target's postion feedback in real time. Toward free flying target catching, We propose a guidance time optimal MPC (model predictive control)algorithm which can be used in trajectory planning of the quadrotor. Based on the receding-horizon optimization strategy, this algorithm can generate time optimal trajectory in every control cycle under the guidance of the time optimal trajectory in the relaxing constrains. In order to avoid obstacles in the pursuing path, a dynamic linear constrain of the obstacle is also presented, which can improve the computationally efficient. Combining with the dynamic linear constrain of the obstacle, the proposed algorithm can generated trajectory that can avoid obstacle reactively while catching up with the target in the minimum time. Simulation results show the validity of the proposed algorithm, and the higher computationally efficiency make it possible to apply it in the real system.