Density functional theory calculations were performed to examine the geometries, electronic structures and thermodynamic properties of high hydrogen storage performances media of Co and Pt functionalized two different sites of carbon doped h-BN nanosheets named CB-doped and CN-doped h-BN. Fundamental aspects such as interaction energy, frontier orbitals, natural bond orbital, charge transfer, molecular electrostatic potential and the partial density of states are demonstrated to analyze the adsorption properties of H2 molecules. The Co-CB-BN, Co-CN-BN, Pt-CB-BN, and Pt-CN-BN systems yielded the gravimetric densities 12.958, 11.833, 4.937 and 4.944%, respectively. Our results revealed that H2 molecules are introduced sequentially on the Co and Pt that decorated upper and lower of CB-doped h-BN and the H2 uptake capacity are found to be 24.909 and 10.788% respectively, well above the gravimetric DOE target is achievable. In addition, two binding mechanisms contribute to the adsorption of hydrogen molecules have been discussed: (i) polarization of the H2 under the electric field produced by the decorated Co and Pt (ii) hybridization with σ orbitals of H2. The hydrogen desorption enthalpy and temperatures suggest that the Co and Pt at CB-doped and CN-doped BN are easy to desorb hydrogen molecules. These results lead to open a prospect of a promising and excellent nanostructural system to enhance the hydrogen storage performances at ambient temperature with application to fuel cells. Finally, unless the attack of oxygen, water and carbon monoxide to the surface is restricted, its strong binding to the design frameworks will block any practical application site for hydrogen storage.