A simple model is presented to describe the phase behavior in binary mixtures of a flexible polymer and a liquid crystal. By using the incompressible approximation to the Onsnger theory which combined both the excluded volume interactions between the liquid crystals and the attractive interaction due to the alignment of the liquid crystals, we obtain the free energy of mixing of the binary mixtures. The derived free energy consists of two terms : the free energy of mixing of Flory-Huggins type for polymer blends and the free energy change due to the alignment of the liquid crystals. We predict the nematic-isotropic phase separation and the isotropic-isotropic one with a critical point in terms of the flory-Huggins and Maier-Saupe interaction parameters. The results are compared with the observed phase diagrams. We also discuss the phase separation in solutions of rigid-rodlike molecules.