Polymer-based nanocomposites such as polycaprolactone/graphene oxide (PCL/GO) have emerged as alternatives for bone tissue engineering (BTE) applications. The objective of this research was to investigate the impact of a gelatin (Gt) coating on the degradability and different properties of PCL nanofibrous scaffolds fabricated by an electrospinning technique with 1 and 2 wt% GO. Uniform PCL/GO fibers were obtained with a beadless structure and rough surface. PCL/GO scaffolds exhibited an increase in their crystallization temperature (Tc), attributed to GO, which acted as a nucleation agent. Young’s modulus increased by 32 and 63% for the incorporation of 1 and 2 wt% GO, respectively, in comparison with neat PCL. A homogeneous Gt coating was further applied to these fibers, with incorporations as high as 24.7 wt%. The introduction of the Gt coating improved the hydrophilicity and degradability of the scaffolds. Bioactivity analysis revealed that the hydroxyapatite crystals were deposited on the Gt-coated scaffolds, which made them different from their uncoated counterparts. Our results showed the synergic effect of Gt and GO in enhancing the multifunctionality of the PCL, in particular the degradability rate, bioactivity, and cell adhesion and proliferation of hGMSC cells, making it an interesting biomaterial for BTE.