A phase diagram for a mixture of polystyrene (PS) and monomeric liquid crystal (E7) was established on the basis of differential scanning calorimetry and cloud point measurements. An upper critical solution temperature (UCST) type phase diagram, overlapping with a nematic-isotropic transition of liquid crystals, was observed. Several deep temperature quenches were undertaken at an off-critical compositon (60/40 PS/E7) from a single phase to a two-phase region. Time-evolution of the structure factor was determined by time-resolved static light scattering. Phase separation appeared to occur via spinodal decomposition (SD) with a growth exponent of 1/3 at deep quenches in conformity with the cluster dynamic theory. A nucleation and growth (NG) was discerned at a shallower temperature quench.