Abstract: On the basis of the generalized Gibbs free energy model for mixing of liquids proposed by the authors in another paper, a non - local - composition activity coefficient equation with two parameters is derived. It is applicable to various small molecule liquid mixtures and polymer solutions, and can be used to predict the VLE of multi - component systems with the binary parameters. The calculated results of the bubble point for small molecule liquid mixtures show that the calculated accuracy is comparable to local -composition - activity coefficient equations, except for the alcohol/hydrocarbon systems. Its applicability to the VLE of polymer solutions is evidently superior to UNIQUAC equations etc.