A kind of new carbon-based material called cup-stacked carbon nanotubes decorated by Pt atom (CSCNTs-Pt) is analyzed to hydrogen adsorption by density functional theory (DFT). The electron density difference, partial density of states, and electrostatic potential are used to display hydrogen adsorption behaviors on CSCNTs-Pt substrate. The optimization results show that only one hydrogen molecule can be chemically adsorbed by the polarization effect of Pt and the others are physically lateralized by Kubas interaction where HH bond lengths of adsorbed hydrogen molecules are increased. Moreover, the hydrogen molecule near the end of the cone axis is hard to chemisorption due to curvature. Compared with planar graphene, single-wall carbon nanotubes, and nanocones, up to eight hydrogen molecules can be accommodated under the substrate because the ninth hydrogen molecule breaks original adsorption stability. With the increase of hydrogen molecules from one to eight, Pt electron transfer is promoted with enhanced orbital hybridization. Display omitted •The Multiple H2 adsorption behavior on CSCNTs decorated by Pt atoms is studied.•The CGL-Pt substrate can adsorb up to eight hydrogen molecules, and HH bond of all molecules are stretched.•Only one hydrogen molecule is adsorbed by polarization, while others by Kubas coordination.•The chemisorbed hydrogen molecule on the CGL-Pt substrate is separated into two hydrogen atoms.•An increase in Hydrogen molecule numbers exacerbates Pt electron transfer.