For the flexible joint manipulator state observer, proposes a model-free nonlinear observer based on neural network in the situation of uncertain model parameters and complex nonlinear friction damping parameter. By radial basis function neural network online approximation, the the neural network weight adaptive law are deduced by Lyapunov stability theory; Through introducing the robust terms to suppress the neural approximation error, accelerates the convergence rate of state observing error; Simulation analysis with different excitation verifies the effectiveness of the proposed method.