The adsorption of molecular hydrogen on the monolayer graphene sheet under varied temperature and pressure was studied using molecular dynamics simulations (MDS). A novel method for obtaining potential energy distributions (PEDs) of systems was developed to estimate the gravimetric density or weight percentage of hydrogen. The Tersoff and Lennard–Jones (LJ) potentials were used to describe interatomic interactions of carbon–carbon atoms in the graphene sheet and the interactions between graphene and hydrogen molecules, respectively. The results estimated by the use of novel method in conjunction with MDS developed herein were found to be in excellent agreement with the existing experimental results. The effect of pressure and temperature was studied on the adsorption energy and gravimetric density for hydrogen storage. In particular, we focused on hydrogen adsorption on graphene layer considering the respective low temperature and pressure in the range of 77–300 K and 1–10 MPa for gas storage purpose which indicate the combination of optimal extreme conditions. Adsorption isotherms were plotted at 77 K, 100 K, 200 K, and 300 K temperatures and up to 10 MPa pressure. The simulation results indicate that the reduction in temperature and increase in pressure favor the gravimetric density and adsorption energies. At 77 K and 10 MPa, the maximum gravimetric density of 6.71% was observed. Adsorption isotherms were also analyzed using Langmuir, Freundlich, Sips, Toth, and Fritz–Schlunder equations. Error analysis was performed for the determination of isotherm parameters using the sum of the squares of errors (SSE), the hybrid fractional error function (HYBRID), the average relative error (ARE), the Marquardt’s percent standard deviation (MPSD), and the sum of the absolute errors (SAE).