Abstract: Input variable selection has many applications in the problem of multivariate time series. In this paper, a novel stepwise variable selection algorithm is proposed based on the k-nearest mutual information estimation. Two steps are used to select the relevant variables and discard weak relevant variables. Meanwhile, the proposed variable selection algorithm is applied to the optimal structure design for radial basis function (RBF) neural networks. The hidden neurons are selected based on K-means clustering and the correlation between the hidden neuron weight and the output, to the purpose that the architecture and the performance of the networks can be improved. Simulation results of Friedman data show the validity of the proposed input variable selection algorithm. Simulation results of Gas furnace and Boston housing substantiate that the size of the improved RBF networks can be controlled on the basis of the model accuracy assured.