An investigation on the crystallization of composites based on poly(ethylene succinate) and unmodified single-walled carbon nanotube was made in this report. Both isothermal and non-isothermal modes were studied along with subsequent melting behavior using differential scanning calorimetry. Crystal morphology was then explored using X-ray scattering and infrared spectroscopy. It was observed during isothermal crystallization that carbon nanotube (CNT) could contribute to the crystallization rate through heterogeneous nucleation. Furthermore, nanotubes enhanced the crystallinity within low and high undercooling rather than medium undercooling. Similar findings were obtained in non-isothermal crystallization mode. At lower cooling rates, the crystallization rate was more strongly influenced by the nanotubes, while at higher cooling rates the crystallinity was affected to the greater extent. The onset of the cold crystallization of polymer remained unaffected in presence of the nanotube, while its extent was reduced. X-ray diffraction together with infrared spectroscopy found that the polymer crystalline morphology was of α type, and no transition from α to β occurred in presence of the CNT.