The development of new biodegradable biomaterials with osteoconductive properties for bone tissue regeneration is one of the urgent tasks of modern medicine. In this study, we proposed the pathway for graphene oxide (GO) modification with oligo/poly(glutamic acid) (oligo/poly(Glu)) possessing osteoconductive properties. The modification was confirmed by a number of methods such as Fourier-transform infrared spectroscopy, quantitative amino acid HPLC analysis, thermogravimetric analysis, scanning electron microscopy, and dynamic and electrophoretic light scattering. Modified GO was used as a filler for poly(ε-caprolactone) (PCL) in the fabrication of composite films. The mechanical properties of the biocomposites were compared with those obtained for the PCL/GO composites. An 18–27% increase in elastic modulus was found for all composites containing modified GO. No significant cytotoxicity of the GO and its derivatives in human osteosarcoma cells (MG-63) was revealed. Moreover, the developed composites stimulated the proliferation of human mesenchymal stem cells (hMSCs) adhered to the surface of the films in comparison with unfilled PCL material. The osteoconductive properties of the PCL-based composites filled with GO modified with oligo/poly(Glu) were confirmed via alkaline phosphatase assay as well as calcein and alizarin red S staining after osteogenic differentiation of hMSC in vitro.