In this paper, the robust adaptive controller design scheme is studied for nonlinear systems in the presence of bounded disturbances A new robust adaptive controller is designed using high-order neural networks, which avoids the singularity problem in adaptive nonlinear control. The stability of the resulting adaptive system with the proposed adaptive controller si guaranteed by suitably choosing the design parameters and initial conditions. I addition, the proposed adaptive controller provides improved transient performance and fast on-line adaptation. The ability and effectiveness of the proposed adaptive control scheme is shown trough simulations of a simple nonlinear system.