A hybrid grand-canonical Monte Carlo simulation has been performed to investigate the hydrogen hydrate compounds in which hydrogen molecules are stored in ice II and ice I(c). A simple theoretical model, which can reproduce the simulation results, provides the phase diagrams of the two-component system in the pressure-composition plane. Stability enhancement of the two ice forms by hydrogen is quantified by the chemical potential calculation of water. The phase transitions among various phases including the two hydrogen hydrates are predicted as functions of pressure, hydrogen occupancy, and temperature.