The adaptive finite-time H_∞ tracking control problem is considered for a motor-driven single-link manipulator system with output constraint in this paper.A new concept on finite-time bounded-H_∞ performance is proposed.And a design method for adaptive neural finite-time bounded-H_∞ tracking controller of the manipulator system with output constraint is given by combining barrier Lyapunov function,neural network adaptive technique,finite-time control theory with H_∞ control theory.The singularity problem emerged in many references with regard to finite time control is avoided when the controller is designed.The purpose of finite-time bounded-H_∞ trajectory tracking control for the manipulator system is achieved.The designed controller can guarantee that the tracking error of the system is constrained by predefined boundary,and all the system states can converge into the neighborhood of the equilibrium state within a finite time.The influence of external disturbances can be attenuated by H_∞ performance at the same time.The simulation results verify the effectiveness and superiority of the designed controller.