Aiming at the problem of systems' simulation that input and output are all continuous time-varying functions, a new method of neural networks modeling which expands based on functions is proposed in this paper. A group of advisable basis functions is selected in continuous function space, and the input and output functions are respectively represented as the expansion form of limited basis functions within the specified precision. Neural networks constitute the conversion relationship between the expansion term coefficient of the basis function of input functions and output functions by learning the training samples. Because there is a one-to-one correlation between the input and output function and the expansion term coefficient, the insinuation relationship between the input and output of the continuous system can be carried out. The implementation methods based on Walsh conversion is given, and the effectiveness of this method is proved by tertiary oil recovery procedure simulation in oil field development.