The traditional fault diagnosis methods have difficulty in accurately extracting fault characteristics in the case of complex power grids, and the fault diagnosis methods with high adaptability and recognition rates are urgently needed. A power grid fault diagnosis method based on the combination of compressed sensing, parallel convolutional neural network (CNN) and long short-term memory (LSTM) is proposed. A model of Yongfu DC transmission system is built to collect raw fault data, and the raw fault data are compressed and sampled by applying the principle of compressed sensing to obtain compressed domain fault signals to improve the computational efficiency of the network. Then, a parallel CNN-LSTM deep learning model with sparrow search algorithm (SSA) is built. The network structure and parameters of the parallel CNN-LSTM are determined by the SSA. The parallel CNN-LSTM deep learning model is used to mine the fault waveform and timing features directly in the compressed domain of the fault and identify the fault. The simulation results verify that the model has higher fault diagnosis accuracy compared with the traditional methods.