The statistical-mechanical local composition model has been applied to describe the composition dependence of a recently developed equation of state for use in vapor-liquid equilibria calculations. The composition-dependence for the mixture properties is derived from a local composition model expression for the Helmholtz free energy. The local composition mixing rules have been tested for a wide variety of binary mixtures: mixtures containing carbon dioxide, acetone, hydrogen sulfide, ammonia, methanol, ethanol, 1-propanol, water, etc. When compared with the conventional conformal solution model, a significant improvement is obtained for vapor-liquid equilibria predictions for strongly nonideal mixtures. This local composition model can be used to extend any corresponding-states type equation of state to mixtures.