To meet the demands of the modern power system for satisfactory operation and control, here, a novel data-driven control strategy is proposed to solve the load frequency control (LFC) problems of power systems, with complete convergence analysis. This data-based LFC approach is designed based on the simultaneous perturbation stochastic approximation (SPSA) method and neural network ensemble. The data-based controller is constructed using a function approximator, which is fixed as a neural network. Being the control parameters, the connection weights of the neural network controller are updated at each iteration step. In order to improve the overall control accuracy and get more stable control performance, the idea of neural network ensemble is introduced for the data-based controller structure design. The proposed data-based controller takes past and current system information as input and generates a control signal that can affect future system performance as output, and during the whole process, it is not necessary to build mathematical model for the controlled plant. A one-area LFC problem with system parametric uncertainties as well as a typical two-area LFC problem have been introduced for simulation tests, and the feasibility and effectiveness of this newly proposed data-based LFC strategy is well revealed through simulation results.