Multiscale entropy is a recently developed method to estimate complexity associated with the long-range temporal correlation of a time series. Since sleep EEG patterns also change regularly from light to deep sleep states, we firstly applied multiscale permutation entropy (MPE) to analysis sleep EEG to investigate the relations between changes of sleep stages and the MPE values. It was observed that correlation coefficient between the averaged MPE values of sleep EEG and the manual scoring of sleep stages can reach over 0.7. Then a MPE-based sleep scoring method for single channel EEG was developed. After training based on the data from 10 subjects, the overall sensitivity of the proposed automatic sleep scoring method combining MPE, autoregressive models, and linear discriminant analysis can reach 89.1% evaluated by the data of the other 10 subjects. Due to high accuracy and requiring only single-channel EEG, the proposed method has good applicability for sleep monitoring and home cares.