A new thermodynamic calculation procedure is introduced to predict the equilibrium conditions of multicomponent gas hydrates containing hydrogen. This new approach utilizes an excess Gibbs potential term to account for second- or higher-order water-cavity distortions due to the presence of multiple guest species. The excess Gibbs potential describes changes in reference chemical potentials according to different compositions of guest mixtures in the hydrate phase. To determine the equilibrium conditions of multicomponent gas hydrates, the excess Gibbs potential term is incorporated to the Lee-Holder model along with the Zele-Lee-Holder cell distortion model. For binary gas hydrates between hydrogen and the other gas molecule, the predicted equilibrium pressure deviates within 10-20% from the experimental value. For the ternary and quaternary mixture hydrates, the model prediction is reasonably good but its error increases with increasing pressure and temperature under the presence of THF.