Automated sleep grading is an alternative to the time-consuming gold standard manual scoring system. Most existing methods use convolutional layers and recurrent-based architectures to build sleep-scoring systems. In this paper, we proposed a sleep stage classification method using the single-channel ECG, which is called ECG-SleepNet. After data preprocessing, we designed CNN layers, SE blocks, and LSTM layer for feature extraction, and multi-head attention mechanism for temporal context encoder, then we used weighted cross entropy as class-aware loss of the classifier. Finally, feedback regulation mechanism to perform the three classification of sleep stages – wake, non-rapid eye movement, and rapid eye movement. We conducted experiments on the Haaglanden Medisch Centrum sleep staging dataset which achieved overall accuracy of 79.98% and kappa score of 0.61. Our comparative experiments with similar studies showed that our model was superior to most other studies. The performance of our method also confirms that the features captured by multi-head self-attention and class-aware loss function are useful for sleep staging.