Tissue engineering aims at fabricating biological substitutes to improve, repair, and regenerate failing human tissues or organs. Designing a nanocomposite scaffolds with tailored properties that enhance the development of functional tissue can be an appropriate approach to achieve this purpose. In this study, the uniform and bead-free nanofibers of poly(epsilon-caprolactone) composited with different graphene oxide nanosheet contents (ranging from 0.5 to 2wt%) were successfully fabricated through electrospinning process. A decrease in the average diameter of poly(epsilon-caprolactone) nanofibers was observed with the addition of graphene oxide nanosheets. Moreover, the nanocomposite scaffolds containing 2 wt% of graphene oxide nanosheets exhibited superior mechanical properties compared to that of pure poly(epsilon-caprolactone). Compared with pure poly(epsilon-caprolactone) scaffold, the degradation rate of poly(epsilon-caprolactone)-graphene oxide nanosheet nanofibers was enhanced, while the integrity of fibers was preserved. The presence of graphene oxide nanosheets in poly(epsilon-caprolactone) fibers promoted in vitro biomineralization, indicating bioactive features of the nanocomposite scaffolds. Compared to the pure one, nanocomposite fibers also showed better ability in protein adsorption. The in vitro cell culture studies showed that the addition of graphene oxide nanosheets did not diminish the biocompatibility of the electrospun poly(epsilon-caprolactone) nanofiber. Furthermore, the adhesion and proliferation of MG63 cells were increased. Altogether, the results demonstrated that electrospun poly(epsilon-caprolactone)-graphene oxide nanosheet nanofiber may be a suitable candidate for tissue engineering scaffold applications.