In the present study, porous (about 70 vol%) nanocomposite scaffolds made of polycaprolactone (PCL) and different amounts (0 to 15 wt%) of 45S bioactive glass (BG) nanoparticles (with a particle size of about 40 nm) containing 7 wt% strontium (Sr) were fabricated by solvent casting technique for bone tissue engineering. Then, a selected optimum scaffold was coated with a thin layer of chitosan containing 15 wt% Sr-substituted BG nanoparticles. Several techniques such as X-ray fluorescence spectroscopy (XRF), X-ray diffraction (XRD), scanning electron microscopy (SEM), dynamic light scattering (DLS), Fourier-transform infrared spectroscopy (FTIR), tensile test, and water contact angle measurement were used to characterize the fabricated samples. In vitro experiments including degradation, bioactivity, and biocompatibility (i.e., cytotoxicity, alkaline phosphate activity, and cell adhesion) tests of the fabricated scaffold were performed. The biomedical behavior of the fabricated PCL-based composite scaffold was interpreted by considering the presence of the porosity, Sr-substituted BG nanoparticles, and the chitosan coating. In conclusion, the fabricated chitosan-coated porous PCL/BG nanocomposite containing 15 wt% BG nanoparticles could be utilized as a good candidate for bone tissue engineering.