A novel biodegradable polymer elastomer nanocomposite composing of poly(1,8-octanediol-citrate) (POC) polymer matrix and carbon nanotubes (CNTs) additive was successfully fabricated and systematically investigated using Fourier transform infrared (FT-IR), X-ray diffractometer (XRD), differential scanning calorimetry (DSC), tensile test, incubation and cytotoxicity tests. It was found that the addition of CNTs in POC elastomer did not result in any noticeable change in its chemical structure and the amorphous state. However, the tensile strength and elongation at break were greatly improved by the addition of CNTs in POC polymer matrix. It revealed that the swelling ratio and percentage of weight loss of POC/CNTs nanocomposite were lower, compared with the pure POC material. Moreover, the adsorption amount of bovine serum albumin (BSA) increased with an increase of the CNTs mass content in POC matrix revealing the enhanced hydrophilicity of POC/CNTs nanocomposites contributed by the carboxyl of the CNTs. Additionally, the cytotoxicity tests with L929 cell line revealed that the experimental POC/CNTs nanocomposites possessed good in vitro biocompatibility.