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With the development of industrialization, the importance of equipment fault prediction is increasing day by day. A fault prediction algorithm based on Recurrent Neural Network (RNN) is proposed. The fitting ability of RNN to time series data is fully explored through data training. The fault prediction model of the RNN is composed of a data processing module and a neural network recognition module. In the data processing module, the method of mathematical function assignment is used to build the training and test samples of the RNN model. In the Neural network recognition module, due to the problem that the change point in current fault prediction technology is difficult to determine, a neural network training method based on successive approximation is used. At last，the RNN fault prediction algorithm is verified by Gas insulated switchgear（GIS） fault data. The results show that the trend of fault can be detected by this method before it occurs, the fault prediction can be realized, and the change point can be located in the gradual approximation training.