In our previous study, we proposed a new expression for the configurational energy of mixing taking into account non-random mixing effect and chain-length dependence of the polymer. But our model can not predict lower critical solution temperature (LCST) behaviours of liquid-liquid equilibria for binary polymer solutions.In this study, we extend our previous model to describe LCST behaviours of binary polymer solutions by employing a secondary lattice concept as a perturbation term to account for oriented interactions (or specific interactions).