Liquid-liquid thermally induced phase separation of the polymer-diluent system of poly(ethylene-co-vinyl alcohol) (EVOH)-glycerol was examined under light scattering. For EVOH with an ethylene content of 38 mol % (EVOH38), maxima of the scattered light intensity were observed that indicated that phase separation occurred by the spinodal decomposition (SD). The growth of the structures formed by the general liquid-liquid phase separation obeyed a power-law scaling relationship in SD. For EVOH with an ethylene content of 32 mol % (EVOH32), the liquid-liquid phase separation resulted from the polymer crystallization. In this case, the structure growth showed the characteristic behavior in which the crystalline particles were initially formed, and then the droplets formed by the liquid-liquid phase separation induced by the crystallization grew rapidly. Furthermore, the growth of the droplet by the phase separation was followed by an optical microscope measurement at a constant cooling rate. The phase-separated structure formed after the crystallization can grow faster than that formed by the normal liquid-liquid phase separation.