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[Display omitted] • The average calculated error between model estimation and viscosity experimental data for pure ILs has been obtained 5.27%. • The mixture viscosity of IL-IL and IL-solvent has been correlated using the Eyring theory coupled with the SAFT-VR Morse model. • The viscosity deviation of the IL-IL mixture has been predicted at different temperatures. This work aims to calculate the viscosities of ionic liquid mixtures using the Eyring theory combined with the SAFT-VR Morse EOS. The free volume theory was used to correlate the pure viscosity of ionic liquids (ILs) and solvents. Three model parameters have been adjusted using experimental viscosity data of ILs between 282 K and 413 K and 1 bar to 350 bar. The average ARD%, Bias%, and rmsd between model estimation and viscosity experimental data for pure ILs have been obtained 4.9 %, 1.015 %, and 0.67, respectively. The average error of the proposed model tends to increase at a pressure higher than 200 bar. The average ARD% for [C 2 mim][Tf 2 N] and [C 6 mim][Tf 2 N] is about 3.8 % and 3.4 % at pressures lower than 200 bar, while the average ARD% values increase sharply at higher pressures. This is due to the weak performance of the SAFT-VR Morse EOS for the calculation of IL density at high pressures. The SAFT-VR Morse EOS has been coupled with the Eyring theory, and the Redlich-Kister mixing rule to estimate the mixture viscosity of ILs-ILs and ILs-solvent systems. The thermal contribution of excess activation free energy has been calculated using the Redlich-Kister mixing rule with four adjustable parameters. The average ARD%, rmsd, and Bias% for fifteen binary mixtures have been obtained 3.9 %, 2.51, and 0.57 %, respectively. The average error values for mixture viscosity of ILs-polar solvent are higher than non-polar solvents. In the case of binary IL-IL systems, the model results are in good agreement with experimental data. The model performance has been evaluated using the viscosity deviation property. The SAFT-VR Morse EOS predicts the negative viscosity deviation. The strong attractive interaction in the mixture than a pure component is the major contribution to negative viscosity deviation. The results show that the new model can calculate the mixture viscosity and viscosity deviation of binary systems satisfactory. The obtained error values of mixture viscosity show that the Eyring theory can be coupled with a SAFT-based EOS to calculate the viscosity of ILs over a wide range of pressures and temperatures satisfactory. [ABSTRACT FROM AUTHOR]