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 δ and fast-σ 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 δ 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 δ and fast-σ 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.