The aim of this study is to design a classifier for sleep stage analysis and select important feature set which shows sleep stage well based on physiological signals during sleep. Sleep has a significant effect on the quality of human life. When people undergo lack of sleep or sleep-related disease, they are likely to reduced concentration and cognitive impairment affects, etc. Therefore, there are a lot of research to analyze sleep stage. In this study, after acquisition physiological signals during sleep, we do pre-processing such as filtering for extracting features. The features are used input for the new combination algorithm using genetic algorithm(GA) and neural networks(NN). The algorithm selects features which have high weights to classify sleep stage. As the result of this study, accuracy of the algorithm is up to 90.26% with electroencephalography(EEG) signal and electrocardiography(ECG) signal, and selecting features are alpha and delta frequency band power of EEG signal and standard deviation of all normal RR intervals(SDNN) of ECG signal. We checked the selected features are well shown that they have important information to classify sleep stage as doing repeating the algorithm. This research could use for not only diagnose disease related to sleep but also make a guideline of sleep stage analysis.