A kind of radial basis statistical network (RBSN) over data stream is proposed based on traditional radial basis function network. The RBSN adopts a compound and multidimensional Gaussian function to fit probability densities of different areas located in input space. The learning algorithm of RBSN is designed based on a mathematical statistics method. Both the time complexity and space complexity of the network learning algorithm are linear with the product of the dimensionality of input variables and the number of hidden units, which are irrelative with the scale of data stream. Therefore, the learning algorithm of RBSN can satisfy the real-time requirement of the analysis of data stream. Simulation results show that the proposed RBSN can effectively solve both regression and classification problems over data stream.