Bone tissue engineering with the aim of repairing bone defects and bone injuries has been trying to design an appropriate scaffold with optimal mechanical and biological properties that can play an important role in this regard. In this study, different amounts of amine-functionalized single-walled carbon nanotubes (SWCNTs-amine) with the 0, 0.1, 0.2 and 0.5 weight percentages (%wt) were added to polycaprolactone, to enhance biological and mechanical properties of scaffolds, then PCLSWCNTs composite nanofibers were prepared by electrospinning method. The attachment, proliferation,  differentiation and growth of rat bone marrow derived mesenchymal stem cells (BMSCs) on the scaffolds were analyzed by scanning electron microscopy (SEM), MTT, live-dead and alkaline phosphatase activity assays. The morphology and mechanical properties of the scaffolds, using the SEM and tensile strength test, were characterized and the bioactivity of the scaffolds in simulated body fluid (SBF) was assessed. The results indicated that PCL-SWCNTs 0.2 wt. % had the highest tensile strength (about 10 MPa) and showed a significant increase as compared with the pure PCL. Moreover, no toxicity was reported after 1, 3 and 5 days after cell seeding on scaffolds. In addition, surveys carried out by SEM showed that the use of single-walled carbon nanotubes, had promoted cell attachment on the scaffold fibers. This increase was more considerable in PCL-SWCNTs 0.5 wt. %. Furthermore, alkaline phosphatase activity demonstrated enhanced proliferation and differentiation of cells on scaffolds containing nanoparticles in comparison with the pure PCL. It is concluded that electrospun SWCNTs/PCL nanofibers with the optimum concentration can be a good candidate for bone tissue engineering applications.