In the present work, the equilibrium solubility of carbon dioxide (CO2) in mixtures of N-methyldiethanolamine (MDEA) and 1-butyl-3-methylimidazolium acetate ionic liquid ([bmim][acetate]) is measured at temperatures (303.15 to 343.15)K and over a pressure range of (0.1 to 3.9)MPa. The mass fraction compositions of the MDEA and [bmim][acetate] in the mixture are (0.3,0.7) and (0.5,0.5), respectively. The experimental results are presented as the partial pressure of CO2 against its molality (mol CO2 per kg of solvent) and mole fraction of CO2. Moreover, using the measured values, the enthalpy of solution for the CO2 solubility in the mixtures is calculated. Considering the present results at the given conditions, it is observed that replacing the aqueous media of the MDEA solution by [bmim][acetate] can reduce significantly the enthalpy of solution of CO2 in the solvent.For thermodynamic modelling, a new equation of state (PR-TS EoS) is extended by combining the Peng–Robinson (PR) equation of state as a cubic term for non-specific energy contribution and the Two-State Association Model (TSAM) for association energy contribution based on the frame of the cubic plus equation of state. Furthermore, the PR-TS EoS is applied to correlate the new experimental data of this work. To model the ternary (CO2+MDEA+[bmim][acetate]) system, the parameters of the PR-TS EoS are first adjusted for the pure components. Subsequently, the solubility of CO2 in pure [bmim][acetate] is correlated so that the binary molecular interaction parameters for this binary sub system are optimised. Finally, the equilibrium solubility of CO2 in ternary mixture of {MDEA+[bmim][acetate]} correlates with the per cent average absolute deviation (AAD%) of 11.78 between the calculated and experimental partial pressure of CO2.