The prediction of stack output power in solid oxide fuel cell (SOFC) systems is a key technology that urgently needs improvement, which will promote SOFC systems towards high-power multi-stack applications. The accuracy of power prediction directly determines the control effect and working condition recognition accuracy of the SOFC system controller. In order to achieve this goal, a genetic algorithm back propagation (GA-BP) neural network is constructed to predict output power in the SOFC system. By testing 40 sets of sample data collected from the experimental platform, it is found that the GA-BP method overcomes the limitation of the traditional back propagation (BP) method—falling into local optima. Further analysis shows that the average relative error of GA-BP has decreased to 1%. The reduction of the relative error improves the accuracy of the prediction results and the average prediction accuracy. Compared with the long short-term memory (LSTM) and BP algorithm, the GA-BP prediction model significantly reduces the relative error of power output prediction, which provides a solid foundation for multi-stack SOFC systems.