The search for hydrogen storage materials allowing the storage of hydrogen in its molecular or atomic form at room temperature to meet the multistage targets such as the US Department of Energy (DOE) ultimate gravimetric and volumetric capacities of 6.5 wt% and 50 kg m(-3) is of global importance. Here, it is reported that an amorphized defective fullerene (C-60-(x)) offers a promising solution to this challenge. C-60-(x) immobilized with single-atom platinum has approximate to 14-fold higher surface area accessible for C-H bonds compared to a crystalline C-60, and its micro/meso pores give a approximate to 20-fold larger volume for fast hydrogen transport. Indeed, hydrogen storage via spillover on C-60-(x) through pressure swing at room temperature is experimentally demonstrated to enable high reversible gravimetric (6.8 wt%) and volumetric (64.9 kg m(-3)) capacities, hitherto the highest reversible capacities close to DOE targets at room temperature. Also, the density functional theory calculations show that a key to efficient hydrogen storage is the preservation of a curved sp(2)-type local carbon geometry for spillover, which holds H radicals loosely for fast hydrogen migration. Moreover, H-atom diffusion on the intact region of C-60-(x) is faster than that on the defect region. Furthermore, excellent capacity retention is achieved over repeated hydrogen adsorption/desorption cycles.