The recently developed Enskog-2 sigma model has been extended to correlate and predict the viscosity of simple liquids. The model is based on the Enskog formulation and makes use of two effective diameters to represent two aspects of molecular interactions in Enskog's treatment; namely, the effective diameter representing the excluded volume of a molecule and the effective diameter accounting for the increased probability of collision in comparison to the dilute gas. We have tested the model by analysing the viscosity of six simple fluids (Ar, N-2, O-2, CO2, CH4, and C2H6) in the liquid phase. The model is capable of correlating the liquid viscosity of the studied fluids with the AAD in the range of 0.1-0.7% and with maximum deviation not exceeding 4.6%. We made use of the observed universal behaviour of the effective diameters to show that the viscosities of the fluids studied are conformal to that of argon. Based on this finding the Enskog-2 sigma model can be used in the predictive mode. Under these circumstances it reproduces the viscosity data obtained from the recommended correlations with AAD in the range 0.8-3.2%, depending on the way in which the length scaling parameters are estimated. (C) 2014 Elsevier B.V. All rights reserved.