The development of carbon capture and storage (CCS) methods has attracted the scientific community’s interest, mainly because it is a technology that can act in the control of greenhouse gas (GHG) emissions with the global permanence of the use of fuels fossils. In this sense, the application of hydrates as a CCS method has become a promising alternative compared to other strategies to reduce carbon dioxide emissions in the atmosphere, mainly due to the large capacity of gas storage, in addition to the possibility of recovery of methane from natural gas hydrate reserves (NGHs) while carbon dioxide is stored in these reservoirs. Therefore, this work studied the thermodynamic equilibrium of hydrate considering a ternary system composed of CO2, CH4 and H2O, in order to contribute to its application as a CCS method. For this, the isofugacity criterion was used to determine the three-phase equilibrium curve of the system and the methodology referring to the minimization of the Gibbs energy was chosen to complement the study since this method allows to determine the compositions of a multiphase and multicomponent system robustly and stably. The Soave-Redlich-Kwong cubic (SRK) equation was used to calculate the liquid and gas phases and the Van Der Waals and Platteeuw models were used to describe the solid-phase of the hydrate. The thermodynamic calculus was developed as an optimization problem, using the General Algebraic Modeling System (GAMS) software and the CONOPT4 solver. The results of this research were compared with experimental data available in the literature, allowing to conclude the satisfactory prediction of the behavior of the phase equilibrium of the studied system.