The mixing rule recently developed by using the binary interaction function L-ij(T, x) depending on the thermodynamic state of a given system, coupled with FRKS equation of state, had been successfully used for calculating the excess properties of wide variety of complex systems. In this work, we further indicated that this mixing rule satisfies the invariance condition and tested the capability of this approach for correlating and predicting vapor-liquid equilibria of highly non-ideal systems at high pressure. Fifteen ternary mixtures and their constituent binaries were selected to do the test. The systems selected cover the range from almost ideal to highly non-ideal mixtures. The correlation results of the binary VLE show that for highly non-ideal systems, instead of the single optimum L-ij value, L-ij function has to be used for correlating their VLE quantitatively. The ternary VLE were predicted by using parameters of constituent binaries only. The results show that, in the case of simple systems, both single optimum L-ij value and L-ij function methods predict the VLE with nearly the same accuracy; nevertheless, the L-ij function method shows a slight edge over the single optimum L-ij value method. For the complex systems containing hydrogen, polar and associated components, while the single L-ij method fails to represent their VLE, the L-ij function approach can predict the VLE for all of these complex systems accurately. The predicted results are in good agreement with the experimental data.