The existing automatic sleep staging algorithms have the problems of too many model parameters and long training time, which in turn results in poor sleep staging efficiency. Using a single channel electroencephalogram (EEG) signal, this paper proposed an automatic sleep staging algorithm for stochastic depth residual networks based on transfer learning (TL-SDResNet). Firstly, a total of 30 single-channel (Fpz-Cz) EEG signals from 16 individuals were selected, and after preserving the effective sleep segments, the raw EEG signals were pre-processed using Butterworth filter and continuous wavelet transform to obtain two-dimensional images containing its time-frequency joint features as the input data for the staging model. Then, a ResNet50 pre-trained model trained on a publicly available dataset, the sleep database extension stored in European data format (Sleep-EDFx) was constructed, using a stochastic depth strategy and modifying the output layer to optimize the model structure. Finally, transfer learning was applied to the human sleep process throughout the night. The algorithm in this paper achieved a model staging accuracy of 87.95% after conducting several experiments. Experiments show that TL-SDResNet50 can accomplish fast training of a small amount of EEG data, and the overall effect is better than other staging algorithms and classical algorithms in recent years, which has certain practical value.