In this study, the adsorption of molecular hydrogens (H2) on boron nitride (BN) frameworks was investigated using the density functional theory (DFT) technique. The results of optimized geometric structures revealed that molecular hydrogens were favourably adsorbed on top of nitrogen atoms in the BN monolayers. In addition, the optimized equilibrium geometries were utilized to calculate the electronic structures, including binding energies, energies of the highest and lowest occupied molecular orbitals (HOMO and LUMO), molecular electrostatic potentials (MEPs), and Mulliken atomic charges (MACs). The binding energy values were calculated to be approximately 0.01 eV per molecular hydrogen based on the results. As the number of molecular hydrogens increased in the BN framework, a slight increase was observed in the binding energy value per hydrogen molecule. Furthermore, the HOMO–LUMO gaps were determined with the corresponding energy values of about 6 eV. Regarding the Frontier molecular orbitals (FMOs) diagrams, the electron densities for the HOMOs of the studied systems were primarily focused on the N-edges. Conversely, for the LUMO, the electron density distribution was localized in the B-edges of titled systems. In the context of hydrogen adsorption on BN nanosheets, the MEP maps indicated that hydrogen atoms at the N-edges of the studied systems exhibited the most positive electrostatic potentials in this research. In contrast, surfaces with negative electrostatic potential surfaces were situated in the region close to B-edges. The computed results are consistent with the corresponding Mulliken atomic charge distributions. From the analyses of the Mulliken scheme, all nitrogen atoms displayed negative charge values, and positive charges were found on the boron atoms. The DFT results obtained in this report may serve as the foundation for developing hydrogen storage materials