An adaptive state observer based on modified BP neural network was developed, which can converge the observed state to the truth state without exact knowledge of the nonlinear system. The stability of the state observer was analyzed by Lyapunov direct method. Then the state observer and backstepping controller were designed respectively, so the estimated velocity of observer substituted the actual one, and avoided measurement of velocity signal in actual application. Finally, the effectiveness of control method is verified by simulation and comparison of the twojoint manipulator system.