This research presents the application of predictive regression model such as quadratic regression for estimation of CO2 solubility in deep eutectic solvents namely allyltriphenylphosphonium bromide-triethylene glycol (ATPPB-TEG) into different molar ratios and their aqueous solutions. In doing so, a design of experiment (DOE) was applied based on Taguchi L18 orthogonal array method. Four factors, namely pressure, temperature, molar ratio and water/DES concentration in mixture were selected as input parameters of model. The output parameter of model was the CO2 solubility in terms of mole fraction of CO2 (XCO2). A quadratic regression model was developed after validation and confirmation through several strong approaches. The results disclose that the prediction of developed quadratic regression model is in acceptable agreement with experimental solubility data. The overall R-squared (R2) and absolute relative error (ARE) values of proposed quadratic regression model were 0.9966 and 0.0725, respectively. Moreover, analysis of variance (ANOVA) indicates that pressure is the most significant factor influencing the XCO2. Finally, the signal to noise (S/N) ratio shows that the highest levels for pressure, concentration of DES in mixture, and molar ratio, and lowest level for temperature are the optimal levels of input parameters to obtain the highest CO2 solubility in this system. The developed quadratic regression model and correlation are effective and provide quick, reliable and accurate predictions of CO2 solubility in DESs without carrying out any time consuming, difficult and expensive experimental measurements. To the best of our knowledge, this is the first time a regression model was developed for prediction of CO2 solubility in DESs and their aqueous solutions. © 2017