In this paper, a nonsingular fast terminal sliding mode control algorithm is designed to solve the problems of large chattering and low accuracy in the trajectory tracking of two-link flexible manipulator. Firstly, the dynamic equation of the two-link flexible manipulator is given according to Lagrange equation and energy conservation law. Then, a nonsingular fast terminal sliding mode controller based on the tracking error state equation is designed, in which the hyperbolic tangent function is used instead of the sign function to weaken the influence of chattering. The stability of the closed-loop system is demonstrated using Lyapunov theory. The simulation results show that the proposed control strategy has the advantages of high tracking accuracy and less chattering.