Recently, drug-eluting nanofibrous scaffolds have attracted a great attention to enhance the cell differentiation through biomimicking the extracellular matrix (ECM) in regenerative medicine. In this study, electrospun nanocomposite polycaprolactone (PCL)-based scaffolds containing synthesized graphene oxide (GO) nanosheets and osteogenic drugs, i.e. dexamethasone and simvastatin were fabricated. The physicochemical and surface properties of the scaffolds were investigated through FTIR, wettability, pH, and drug release studies. The cell viability, differentiation, and biomineralization were studied on mesenchymal stem cells (MSCs) by Alamar Blue, alkaline phosphatase (ALP) activity, and Alizarin Red-S staining, respectively. Uniformly distributed GO (thickness < 1 nm) in PCL nanofibers was observed by electron microscopy. It was revealed that the addition of GO and the drugs improved the hydrophilicity, cell viability, and osteogenic differentiation, in addition to pH changes, in comparison with PCL scaffolds. Despite the notable reduction in the cell viability, significant differentiation was revealed by ALP assay on PCL/GO-Dex scaffolds. Noteworthy, a twofold increase in the osteogenic differentiation was observed in comparison with the cells cultured in osteogenic differentiation medium, while a significant biomineralization was observed. The results of this study indicate the synergistic effect of GO and dexamethasone on improving osteogenic differentiation of drug-eluting nanocomposite scaffolds in bone tissue engineering applications.