Deep brain stimulation (DBS) is an established treatment for patients with Parkinson's disease (PD). Sleep disorders are common complications of PD and affected by subthalamic DBS treatment. To achieve more precise neuromodulation, chronic sleep monitoring and closed-loop DBS toward sleep-wake cycles could potentially be utilized. Local field potential (LFP) signals that are sensed by the DBS electrode could be processed as primary feedback signals. This is the first study to systematically investigate the sleep-stage classification based on LFPs in subthalamic nucleus (STN). With our newly developed recording and transmission system, STN-LFPs were collected from 12 PD patients during wakefulness and nocturnal polysomnography sleep monitoring at one month after DBS implantation. Automatic sleep-stage classification models were built with robust and interpretable machine learning methods (support vector machine and decision tree). The accuracy, sensitivity, selectivity, and specificity of the classification reached high values (above 90% at most measures) at group and individual levels. Features extracted in alpha (8-13 Hz), beta (13-35 Hz), and gamma (35-50 Hz) bands were found to contribute the most to the classification. These results will directly guide the engineering development of implantable sleep monitoring and closed-loop DBS and pave the way for a better understanding of the STN-LFP sleep patterns.