Cage occupancies of hydrogen molecules in a clathrate hydrate have been examined by means of semi-grand canonical Monte Carlo simulations where hydrogen molecules enter into or leave from it in the presence of promoter species. This kind of simulation allows to evaluate the thermodynamic stability via the chemical potential of water at a given temperature and pressure. In order to make a better estimation of the chemical potential, we adopt a different standard state from the corresponding empty one. It is revealed that the present method is indeed effective to minimize errors associated with the numerical simulations.