This paper presents an adaptive neural network (NN) control strategy for robot manipulators with uncertainties and constraints. Position, velocity and control input constraints are considered and tackled by introducing barrier Lyapunov functions in the backstepping procedure. The system uncertainties are estimated and compensated by a locally weighted online NN. The boundedness of the closed-loop control system and the feasibility of the proposed control law are demonstrated by theoretical analysis. The effectiveness of the proposed control strategy has been verified by simulation results on a robot manipulator.