Clathrate hydrates of hydrogen are of specific interest due to their potential ability to store molecular hydrogen. In particular, structure H (sH) hydrate has a higher theoretical storage capacity in comparison with the other two more common hydrate structures (sI and sII). This paper investigates the effect of hydrogen (H-2) concentration on the phase equilibria of sH hydrate in a quaternary system of water, methane, hydrogen, and methylcyclohexane. Phase equilibria and cage occupancies of the quaternary system were predicted using the van der Waals and Platteeuw (vdWP) model for different hydrogen/methane ratios ranging from 0 to 7. Model predictions for the quaternary systems were found to be in good agreement with measured experimental data. It was evident from the thermodynamic equilibrium conditions of the quaternary system (MCH + H2O + CH4 + H-2) that as the H-2 concentration increases (H-2:CH4 ratio increased from 0 to 7), higher pressures are required to produce sH hydrates at the same temperature. It was also found that the fractional cage occupancy of CH4 in the small and medium cages of sH hydrate increases with pressure.