Considering the characteristics of the quad-rotor Unmanned Aerial Vehicle (UAV) such as under-actuation, non-linearity, strong coupling and susceptibility to external disturbances, a control method based on fast Terminal Sliding Mode Control (TSMC) is proposed to guarantee the UAV's control quality and precision requirements. The dynamic mathematical model of the quad-rotor UAV in the turbulent wind field is built. The control algorithm of the global fast terminal sliding mode which can automatically eliminate the vibration is used to calculate each control law, and the under-driven coupling control is realized by introducing the control law of transitional input. The system module is constructed and simulated by using Matlab/Simulink software. The simulation results show that the fast TSMC controller algorithm has high reliability, fast convergence speed and strong robustness, which can effectively complete the quad-rotor UAV's flight tasks.