Adsorption of eight numbers of H2, (H2)n where n = 1, 2, 4, 6, 8, 12, 18, 24, adsorbed on the C24N24 nanocage (CNNC) surface was investigated using three different DFT methods. Adsorption energies of various numbers of H2 adsorbed on the CNNC surface were obtained. Adsorption strength of the CNNC was found depending on the adsorbed H2 numbers and is in order: the H2 numbers of (H2) > (H2)2 > (H2)4 > (H2)6 > (H2)8 > (H2)12 > (H2)18 > (H2)24. The most stable adsorption configuration of (H2)12/CNNC, all adsorbed H2 molecules formed as the full monolayer (ML) coverage, are dissociative chemisorption. The bilayer of (H2)24/CNNC was found that the first and second layers are composed of 12H2 as dissociative chemisorption and 12H2 as physisorption, respectively. The high hydrogen storage capacity of the CNNC formed as (H2)24/CNNC, around 7.75 wt% was found.