Sleep is beneficial for various types of learning and memory, including a finger-tapping motor-sequence task. However, methodological issues hinder clarification of the crucial cortical regions for sleep-dependent consolidation in motor-sequence learning. Here, to investigate the core cortical region for sleep-dependent consolidation of finger-tapping motor-sequence learning, while human subjects were asleep, we measured spontaneous cortical oscillations by magnetoencephalography together with polysomnography, and source-localized the origins of oscillations using individual anatomical brain information from MRI. First, we confirmed that performance of the task at a retest session after sleep significantly increased compared with performance at the training session before sleep. Second, spontaneous delta and fast-sigma oscillations significantly increased in the supplementary motor area (SMA) during post-training compared with pretraining sleep, showing significant and high correlation with the performance increase. Third, the increased spontaneous oscillations in the SMA correlated with performance improvement were specific to slow-wave sleep. We also found that correlations of delta oscillation between the SMA and the prefrontal and between the SMA and the parietal regions tended to decrease after training. These results suggest that a core brain region for sleep-dependent consolidation of the finger-tapping motor-sequence learning resides in the SMA contralateral to the trained hand and is mediated by spontaneous delta and fast-sigma oscillations, especially during slow-wave sleep. The consolidation may arise along with possible reorganization of a larger-scale cortical network that involves the SMA and cortical regions outside the motor regions, including prefrontal and parietal regions.