The properties of binary H2 + CH4 clathrate hydrates have been estimated using the extended van der Waals and Platteeuw statistical thermodynamic model that takes into account the lattice relaxation, host-guest, and guest-guest interactions as well as the quantum nature of guest behavior in the clathrate cavities. It has been found that at a small methane concentration in the gas phase the stable hydrate phase has cubic structure II (CS-II) and at a methane concentration of 6% stabilizes cubic structure I, which is metastable in the case of the pure hydrogen hydrate. This is in agreement with recent experimental data. The amount of hydrogen storage depends on the methane concentration in the gas phase as well as the thermodynamic conditions of hydrate formation. Hydrogen storage up to 2.6 wt. % can be achieved in the binary H2 + CH4 CS-II hydrate at T = 250 K.