Designing suitable nano-carriers for simultaneous gene delivery and tracking is in the research priorities of the molecular medicine. Non-toxic graphene quantum dots (GQDs) with two different (green and red) emission colors are synthesized by Hummer's method and characterized by UV-Vis, Photoluminescence (PL), Fourier Transform Infrared (FTIR) and Raman spectroscopies, Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). The GQDs are conjugated with MPG-2H1 chimeric peptide and plasmid DNA (pDNA) by non-covalent interactions. Following conjugation, the average diameter of the prepared GQDs increased from 80 nm to 280 nm in complex structure, and the ζ-potential of the complex increased (from -36.87 to -2.56 mV). High transfection efficiency of the nano-carrier and results of confocal microscopy demonstrated that our construct can be considered as a nontoxic carrier with dual functions for gene delivery and nuclear targeting.