Grand canonical Monte Carlo simulations were performed to study the occupancy of structure I multicomponent gas hydrates by CO2/CH4, CO2/N-2, and N-2/CH4 binary gas mixtures with various compositions at a temperature of 270 K and pressures up to 70 atm. The presence of nitrogen in the gas mixture allows for an increase of both the hydrate framework selectivity to CO2 and the amount of carbon dioxide encapsulated in hydrate cages, as compared to the CO2/CH4 hydrate. Despite the selectivity to CH4 molecules demonstrated by N-2/CH4 hydrate, nitrogen can compete with methane if the gas mixture contains at least 70% of N-2.