G353.273+0.641 is a very young high-mass protostar (~10 solar masses) with a nearly face-on accretion system. Our ALMA long-baseline observation resolved a compact accretion disk of 250 au in radius. The disk has a mass of at least 3 solar masses, which is ~30 percent of the host protostar. We found remarkable grand-design spiral arms in this self-gravitating disk. Toomre’s Q parameter ranges from 0.5-1.0 in the arms, while 1.5-2.5 in the interarm region. The disk showed several local excesses of surface density, suggesting ongoing fragmentation processes. Those local clumps are still less massive (< 0.1 solar masses) but may evolve into companions. Otherwise, they would cause a so-called accretion burst event falling onto the host protostar. We also found a further unresolved structure (30 au in diameter) at the disk center. This inner structure is consistent with a ring traced by infalling methanol masers reported by Motogi et al. (2017). We suggest that this compact structure could trace a nested disk caused by angular momentum transfer via the gravitational torque of the spiral arms. Our new observation first provided direct observational evidence of the highly unstable and variable accretion process in the early accretion phase of high-mass star formation.