The storage of hydrogen is key to its applications. Developing adsorbent materials with high volumetric and gravimetric storage capacities, both of which are essential for the efficient use of hydrogen as a fuel, is challenging. Here we report a controlled catenation strategy in hydrogen-bonded organic frameworks (RP-H100 and RP-H101) that depends on multiple hydrogen bonds to guide catenation in a point-contact manner, resulting in high volumetric and gravimetric surface areas, robustness and ideal pore diameters (~1.2-1.9 nm) for hydrogen storage. This approach involves assembling nine imidazole-annulated triptycene hexaacids into a secondary hexagonal superstructure containing three open channels through which seven of the hexagons interpenetrate to form a seven-fold catenated superstructure. RP-H101 exhibits high deliverable volumetric (53.7 g l-1) and gravimetric (9.3 wt%) capacities for hydrogen under a combined temperature and pressure swing (77 K/100 bar → 160 K/5 bar). This work illustrates the virtues of supramolecular crystals as promising candidates for hydrogen storage.