Sleep electroencephalogram (EEG) is an important index in diagnosing sleep disorders and related diseases. Manual sleep staging is time-consuming and often influenced by subjective factors. Existing automatic sleep staging methods have high complexity and a low accuracy rate. A sleep staging method based on support vector machines (SVM) and feature selection using single channel EEG single is proposed in this paper. Thirty-eight features were extracted from the single channel EEG signal. Then based on the feature selection method F-Score's definition, it was extended to multiclass with an added eliminate factor in order to find proper features, which were used as SVM classifier inputs. The eliminate factor was adopted to reduce the negative interaction of features to the result. Research on the F-Score with an added eliminate factor was further accomplished with the data from a standard open source database and the results were compared with none feature selection and standard F-Score feature selection. The results showed that the present method could effectively improve the sleep staging accuracy and reduce the computation time.