In this paper we present a new model for correlating the dynamic viscosity of Newtonian liquids at high pressures. The proposed model is based on Eyring's absolute rate theory for liquid viscosity and considers the activation energy for viscous flow as being a thermodynamic free energy. The viscosity of the system is described by a combination of a reference term, given by the Chapman-Enskog theory, and a deviation contribution. A virial-type expansion in pressure and a term comprising an expression for the residual Helmholtz free energy of the system account for the deviation from the nonattracting rigid sphere model viscosity behavior. Three cubic equations of state, Peng-Robinson, Soave-Redlich-Kwong, and Peng-Robinson-Stryjek-Vera, have been tested for evaluating the residual Helmholtz free energy. The model requires only two adjustable parameters for each pure liquid, at each temperature. The parameters have been determined by fitting literature viscosity data of 49 different pure liquid compounds from pressures of 0.1-250 MPa within the reduced temperature interval of 0.4-0.7. The performance of the model has been found to be insensitive to the choice of the equation of state, except at pressures above 100 MPa for which only the Soave-Redlich-Kwong equation of state has been able to describe the volumetric behavior of the liquids. The studied liquids are n-alkanes, substituted alkanes, n-alkenes, cyclic alkanes, aromatics, alcohols, esters, 1-butylamine, argon, nitrogen, oxygen, ammonia, and water. The calculated values are in good agreement with the experimental ones. The value of the overall average absolute deviation, for the 4380 data points correlated with the present model, is 1.22%.