We performed first-principles calculations to investigate hydrogen (H2) storage properties of bare and calcium (Ca)-decorated polygon-graphenes, i.e., biphenylene and ψ-graphene monolayers consisting of polygons, from tetragons to octagons. In pristine forms, both biphenylene and ψ-graphene bind H2 weakly. However, upon Ca doping, biphenylene adsorbed up to five H2 molecules regardless of polygonal sites, whereas ψ-graphene anchored up to six and five H2 molecules to pentagonal and heptagonal sites, respectively. In all the cases, the H2 binding energy was ~0.30 eV, enabling reversible room-temperature H2 storage. The H2 storage capacity can reach ~6.8 and ~4.2 wt % for Ca-decorated biphenylene and ψ-graphene, respectively. Using equilibrium thermodynamics, we showed the adsorption and desorption of H2 at 300 and 380 K under ambient pressure, respectively. This clearly indicates that Ca-decorated 2D sp2 carbon sheets with polygons (biphenylene, ψ-graphene) could be used as promising H2 storage materials.