Radial Basis Function Neural Network（ RBF） is widely used now; it can solve the following problems: the small sample, nonlinear, dimension and local minima. Firstly, this paper briefly introduces the basic principles of RBF, and then comprehensively accounts the RBF domestic and overseas study status, discusses the advantages and disadvantages of various methods, and compares the explanation, finally analyzes the existing problems and the development trend in the future.