Sets up an improved SIR model for the spread of influenza A (H1N1), and uses the fourth-order Runge-Kutta method to solve it. Applies the data of Mexico's cases to verify the model, and it shows that the results are basically tallied with the actual data. By comparing the data obtained by SIR model with data of the GM(1,1) gray prediction model and data of second-order and fourth-order curve-fitting, draws a conclusion that the error of SIR model is minimum.