This paper proposes a novel neural-network approach to blind source separation in nonlinear mixture. The approach utilizes a radial basis function (RBF) neural-network to approximate the inverse of the nonlinear mixing mapping which is assumed to exist and able to be approximated using an RBF network. A contrast function which consists of the mutual information and partial moments of the outputs of the separation system, is defined to separate the nonlinear mixture. The minimization of the contrast function results in the independence of the outputs with desirable moments such that the original sources are separated properly. Two learning algorithms for the parametric RBF network are developed by using the stochastic gradient descent method and an unsupervised clustering method. By virtue of the RBF neural network, this proposed approach takes advantage of high learning convergence rate of weights in the hidden layer and output layer, natural unsupervised learning characteristics, modular structure, and universal approximation capability. Simulation results are presented to demonstrate the feasibility, robustness, and computability of the proposed method.