Considering the problems of unmodeled parts, friction and external interference in the practical application of the manipulator, an adaptive exact-time sliding mode control method is proposed to realize the trajectory tracking of each joint of the manipulator. Firstly, the manipulator is modeled, and the unmodeled part, friction force and external disturbance are regarded as concentrated disturbances. Secondly, an exact-time sliding mode surface is designed to overcome the problem of overestimation of the convergence time of the traditional terminal sliding mode surface. Based on this, a global exact-time convergent sliding mode control method is designed for the manipulator system, which enables the manipulator system to achieve stability at the setting time and keep strong robustness after setting time. The upper bound of the disturbance is estimated by an adaptive method to avoid overestimation of the gain. Then a low-pass filter is designed to reduce chattering. Finally, the control method is simulated. The results show that the proposed control method can strictly control the stability time of the manipulator system, reduce the steady-state error, and achieve high-precision trajectory tracking control of the manipulator system.