Aiming at the problem of parameter uncertainty and external interference in the trajectory tracking of quadrotor unmanned aerial vehicle (UAV), a discrete-time fast terminal sliding mode control (FTSMC) scheme is proposed in this paper. Firstly, the position model of the UAV is derived based on the dynamic equation, and the discrete-time model of the UAV is obtained and analyzed by Euler discretization technology. Then, by introducing a new discrete-time fast terminal sliding mode surface, and designing the fast sliding mode terminal control rate based on equivalent control, the UAV can track the desired trajectory with small steady-state error. Finally, in the experimental part, the feasibility and superiority of this scheme are verified by comparing with the traditional PID position control method.