Sleep stage scoring is a hotspot in the field of medicine and neuroscience. Visual inspection of sleep is laborious and the results may be subjective to different clinicians. Automatic sleep stage classification algorithm can be used to reduce the manual workload. However, there are still limitations when it encounters complicated and changeable clinical cases. The purpose of this paper is to develop an automatic sleep staging algorithm based on the characteristics of actual sleep data. In the proposed improved K-means clustering algorithm, points were selected as the initial centers by using a concept of density to avoid the randomness of the original K-means algorithm. Meanwhile, the cluster centers were updated according to the 'Three-Sigma Rule' during the iteration to abate the influence of the outliers. The proposed method was tested and analyzed on the overnight sleep data of the healthy persons and patients with sleep disorders after continuous positive airway pressure (CPAP) treatment. The automatic sleep stage classification results were compared with the visual inspection by qualified clinicians and the averaged accuracy reached 76%. With the analysis of morphological diversity of sleep data, it was proved that the proposed improved K-means algorithm was feasible and valid for clinical practice.