In this paper we propose a radial basis function (RBF) neural network for nonlinear time-invariant channel equalizer. The RBF network model has a three-layer structure which is comprised of an input layer, a hidden layer and an output layer. The learning algorithm consists of unsupervised learning and supervised learning. The unsupervised learning mainly adjusts the weight among input layer and hidden layer. The supervised learning adjusts the weight among output layer and hidden layer. We will implement RBF by using FPGA. Computer simulation results show that the bit error rates of the RBF equalize using software and hardware implements are close to that of the optimal equalizer.