A rapid, environmentally friendly and simple approach is conducted for the synthesis of graphene quantum dots (GQDs) using naturally available biomass materials such as lemon juice and ascorbic acid under supporting of microwave irridiation, at power 900 W and fast reaction time ~9 min. Besides, Ag nanoparticles were successfully combined with GQDs by a simple and easy to implement method, all solvents used here being deionized water with reaction temperature at 60oC for 30 min to form GQDs/Ag nanocomposites. The synthesized GQDs/Ag nanocomposites were determined their properties, morphologies and compositions by: UV-vis, FTIR, XRD, TEM, and EDX. Results showed that the GQDs/Ag nanocomposites were spherical in shape, uniformly distribution, with an average particle size of GQDs and Ag nanoparticles (Ag NPs) respective being ~5-10 nm and ~10-25 nm. The percent (%) component of elements present in the synthesized GQDs/Ag nanocomposites sample were found to be composed mainly including: C (45.36%); O (39.04%); N (3.96%); and Ag (11.05%), respectively. Moreover, the synthesized GQDs/Ag nanocomposites have also applied in glucose detection by photoluminescence (PL) spectroscopy with an extremely low limit of detection (LOD) for glucose concentration being ~10 nM (~10-8 M). Based on experimental results, it indicated that GQDs/Ag sample is a potential and promising nanomaterial, which can be oriented and developed as nanomaterials to apply in many fields such as biomedical sensors, chemical sensors, etc.