Reformulated principle of fault estimation design for one class of first order continuous-time nonlinear system is treated in this paper, where a neural network is regarded as model-free fault approximator. The problem addressed is presented as approach based on sliding mode methodology with combination of radial basis function neural network to design robust nonlinear fault estimation. The method utilizes Lyapunov function and the steepest descent rule to guarantee the convergence of the estimation error asymptotically. Simulation results show the feasibility of the proposed approach.