In this work, a facile green approach for the synthesis of graphene quantum dots (GQDs) embedded on silicate network silver nanocrystals (GQDs-AgNCs(APTS)) is reported. Moreover, glassy carbon-GC electrodes were modified with the prepared nanocomposite containing graphene quantum dots supported on silver nanocrystals (GQDs-AgNCs(APTS)) and applied for simultaneous detection of guanine (GA) and adenine (AD). The chemically modified electrode was assessed during the determination of purine bases by cyclic voltammetry-CV and differential pulse voltammetry-DPV. The incorporation of GQDs-AgNCs(APTS) nanocomposites over the surface of the GC electrode considerably enhances the anodic peak currents and decreases the adenine and guanine peak potentials. Compared to other electrodes, GQDs-AgNCs(APTS)/GC improved the electrochemical behavior towards the detection of adenine and guanine. At optimal conditions, calibration curves were obtained by DPV being linear in the range of 0.1–6.0 μM and 0.1–5.0 μM for guanine and adenine, respectively. The detection limits of both guanine and adenine were estimated as 0.1 μM. Additionally, interferences analyses were performed on the existence of other interferent compounds. Furthermore, the method developed for the identification of GA and AD was proved using fish sperm DNA samples.