Cartilage as a tissue in the body possesses a low regenerative capacity and is extremely difficult to repair. Today, treatment of cartilage injury, degeneration and defects presents critical clinical challenges, yet none of the currently available cartilage treatments provides a perfect solution. Since natural cartilage extracellular matrix is a nanoscaled structure, the main objective of this study is to design a novel biomimetic nanostructured cartilage construct via electrospinning and carbon nanomaterials for enhancing human bone marrow mesenchymal stem cell chondrogenic differentiation. For this purpose, we synthesized a carbon nanomaterial mixture, using a plasma arc discharge method, consisting of graphene nanoplatelets and single walled carbon nanotubes. This nanomaterial was then incorporated into electrospun polycaprolactone (PCL) microfibrous scaffolds, with and without an additional poly-L-lysine surface coating. Scaffolds were thoroughly characterized for both their biomimetic features and biocompatibility. Our results showed that our scaffolds with carbon nanomaterial have greatly improved mechanical properties and enhanced stem cell adhesion, proliferation and chondrogenic differentiation than PCL controls without carbon nanomaterials, and thus hold promise for improving cartilage formation in future in vivo studies and clinical applications.