Nanocomposites based on poly(trimethylene terephthalate)-block-poly(tetramethylene oxide) (PTT-PTMO)-segmented copolymer and COOH-functionalized single-walled carbon nanotubes (SWCNTs) were prepared by in situ polymerization method. The obtained nanocomposites were characterized by thermogravimetric analysis, scanning electron microscopy, differential scanning calorimetry (DSC), DMTA, wide-angle x-ray scattering (WAXS), small-angle X-ray scattering, and tensile testing. The nanocomposites with low SWCNTs loading (<0.5 wt %) shows uniform dispersion of CNT in polymer matrix. As the SWCNTs loading in the nanocomposites increase, the significant improvement of thermo-oxidative stability was observed. It was found that the nanocomposites have slightly higher degree of crystallinity (determined by DSC and WAXS) of poly(trimethylene terephthalate) (PTT) hard phase than neat PTT-PTMO copolymer. The melting point of PTT hard phase and glass transition temperature of poly(tetramethylene oxide)-rich phase were not affected by the presence of CNTs in polymer matrix. The SWCNTs played a role as nucleating agent in PTT-PTMO matrix, which led to increase in the crystallization rate. Tensile tests showed that the tensile strength of the nanocomposites with 0.05-0.3 wt % loading of SWCNTs have improved tensile strength in comparison to the neat PTT-PTMO copolymer without reduction elongation at break.