Molecular dynamics simulations and stabilization energy calculations are performed in this work in order to understand the stability of CH4 hydrate, CO2 hydrate, and CH4-CO2 mixed hydrate. The model systems of fully occupied type SI CH4 hydrate, CO2 hydrate, and CH4-CO2 mixed hydrate are prepared in a simulation box of 2 x 2 x 2 unit cell with periodic boundary conditions. The MD simulation results reveal that the CH4-CO2 mixed hydrate is the most stable one in above three hydrates. The stabilization energy calculations of small and large cavities occupied by CH4 and CO2 show that the CO2 molecule is less Suitable for the small cavity because of its larger size compared with the CH4 molecule but is more Suitable for the large cavity. The results in this work can also explain the possibility of CH4 molecule in reoccupying the small cavity during the replacement of CH4 hydrate by CO2, from the hydrate stability point of view.