The model of speed-governing performance of axial flow pump device was deduced by combining theory with experimental data, and by using multiple nonlinear regression analysis method. The study of the model was aimed at a present situation that there was no speed-governing performance model with clear physical meaning. With this model, the study of speed control strategy can go further. Firstly, the characteristic equation of head, efficiency about speed and flow was deduced by the basic equation of water pump, combined with some assumptions. And then a conclusion that the efficiency and head characteristic curve was shown to be nonlinearly variable by the change of speed which was given by the test of two different types axial flow pump devices on the high-precision hydraulic machinery test bed. The undetermined coefficients of characteristic equation were concluded by multivariate nonlinear regression algorithm combined by ‘nlinfit’ function and genetic algorithm, using experimental data as the observation value, and using the characteristic equation as the predictive model. By comparing ‘nlinfit’ function with genetic algorithm, it was clear that the coefficient solution tended to locally optimum by using ‘nlinfit’ function only. And it tended to globally optimum by combining with genetic algorithm. By comparing the experimental data with prediction model, both of which are of two different types axial flow pump devices’ speedgoverning performance of head and efficiency, it showed that on the whole area, the head error between prediction model and measured value was 0~0.8m, and the efficiency error was 0~8%. On the area nearby the design point, the head error between prediction model and measured value was 0~0.5m, and the efficiency error was 0~5%.