Aiming at the problem that the unbalanced distribution of data in sleep electroencephalogram(EEG) signals and poor comfort in the process of polysomnography information collection will reduce the model's classification ability, this paper proposed a sleep state recognition method using single-channel EEG signals (WKCNN-LSTM) based on one-dimensional width kernel convolutional neural networks(WKCNN) and long-short-term memory networks (LSTM). Firstly, the wavelet denoising and synthetic minority over-sampling technique-Tomek link (SMOTE-Tomek) algorithm were used to preprocess the original sleep EEG signals. Secondly, one-dimensional sleep EEG signals were used as the input of the model, and WKCNN was used to extract frequency-domain features and suppress high-frequency noise. Then, the LSTM layer was used to learn the time-domain features. Finally, normalized exponential function was used on the full connection layer to realize sleep state. The experimental results showed that the classification accuracy of the one-dimensional WKCNN-LSTM model was 91.80% in this paper, which was better than that of similar studies in recent years, and the model had good generalization ability. This study improved classification accuracy of single-channel sleep EEG signals that can be easily utilized in portable sleep monitoring devices.