Bayesian radial basis function neural network is presented to explore the weight structure in radial-basis function neural networks for discriminant analysis. The work is motivated by the empirical experiments where the weights often follow certain probability density functions in protein sequence analysis using the bio-basis function neural network, an extension to radial basis function neural networks. An expectation-maximization learning algorithm is proposed for the estimation of the weights of the proposed Bayesian radial-basis function neural network and the simulation results show that the proposed novel radial basis function neural network performed the best among various algorithms.