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Sliding mode control (SMC) has a strong capability of controlling nonlinear systems with uncertainties. However, the discontinuous control signal causes the significant problem of chattering. Furthermore, it requires thorough knowledge of the parameters and dynamics of the controlled plant, which are difficult to be obtained or may be unknown, to calculate the equivalent control law of SMC. In this paper, a combination of SMC and neural network (NN) is proposed. The weights of NN are adjusted using a backpropagation algorithm. To construct corrective control law of SMC for overcoming the chattering problem, a new and simple approach using a simplified distance function with a modified sliding surface is utilized. Thus, the chattering is eliminated and the performance of SMC is improved. Finally, a brief stability analysis of the proposed method is carried out, and the effectiveness of this method is confirmed through computer simulations.