The research of sleep staging is not only the basis of diagnosing sleep related diseases, but also the precondition of evaluating sleep quality, and has important clinical significance. In recent years, the research of automatic sleep staging based on computer has become a hotspot and made some achievements. Feature extraction and feature classification are two key technologies in automatic sleep staging system. In order to achieve effective automatic sleep staging, we proposed a new automatic sleep staging method which combines the energy features and least squares support vector machines (LS-SVM). Firstly, we used FIR band-pass filter to extract the energy features of Pz-Oz channel sleep electroencephalogram (EEG) signals, and compared them with those from wavelet packet transform method. Then we designed an LS-SVM classifier to realize the automatic sleep stage classification. The research showed that FIR band-pass filter (with the Kaiser window) performed better than wavelet packet transform (WPT) for energy feature extraction just in terms of the data from the Sleep-EDF Database and the LS-SVM classifier (with the RBF Kernel function) designed was good, and the automatic sleep staging method proposed in this paper was better than many similar methods from other studies with an average accuracy of 88.89% and had a very prosperous application future.