The NRTL equation, a well-known excess Gibbs energy model, is frequently used to model thermodynamic properties of coexisting liquid phases. Like all classical equations, the NRTL model neglects the effects of long-range concentration fluctuations on the thermodynamic properties. It is well known however that, near a critical point, a system exhibits long-range fluctuations in the order parameter or, for binary liquids, in the concentration. The NRTL equation, therefore, fails to describe the singular behavior of thermodynamic properties in the critical region. In this work an existing crossover procedure, developed to incorporate critical fluctuations into the classical NRTL equation, has been improved. This crossover-NRTL model has a smooth crossover from universal scaling behavior at the critical point to classical behavior far away from the critical point. The model has been applied to seven different binary liquid systems at constant pressure with different asymmetry of the coexistence curves. The physical significance of the optimized NRTL and crossover parameters is discussed.