Miscibility phase diagrams of mixtures of a side-on side-chain liquid crystalline polymer (s-SCLCP) and low molar mass liquid crystals have been investigated experimentally and theoretically. The theoretical calculation on equilibrium phase diagrams of binary nematic mixtures involves a combination of the Flory-Huggins (FH) free energy for isotropic mixing in conjunction with the Maier-Saupe (MS) free energy for nematic ordering of the mesogenic units. This combined FH-MS theory predicts a variety of phase diagrams depending on relative strength of cross-interaction between two dissimilar mesogens to that in the same species. The s-SCLCP synthesized is polyacrylate with a mesogenic side group connected by a butyl spacer. The temperature-composition phase diagrams of the mixtures of s-SCLCP and eutectic low molar mass liquid crystal (E44 and E48) have been established by a cloud point method. The calculated phase diagrams are found to accord well with the experimental phase diagrams.