Prediction of phase equilibrium behaviors of fluids and fluid mixtures solely from information on functional group interactions remains one of the most intriguing problems. The recent success of quasi lattice description of fluids by the present authors leads us to look into group contribution application of the model. With a size parameter for each group and an interaction energy parameter between groups, equation of state(EOS) parameters for pure fluids and mixtures were calculated. Predicted phase equilibrium properties of pure alkanes, pure alcohols and their mixtures showed good agreements with experimental data.