In this work, a green and simple one-pot route was developed for the synthesis of highly fluorescent amino-functionalized graphene quantum dots (a-GQDs) via hydrothermal process without any further modification or surface passivation. We synthesized the a-GQDs using glucose as the carbon source and ammonium as a functionalizing agent without the use of a strong acid, oxidant, or other toxic chemical reagent. The as-obtained a-GQDs have a uniform size of 3-4 nm, high contents of amino groups, and show a bright green emission with high quantum yield of 32.8%. Furthermore, the a-GQDs show effective fluorescence quenching for Cu2+ ions which can serve as effective fluorescent probe for the detection of Cu2+. The fluorescent probe using the obtained aGQDs exhibits high sensitivity and selectivity toward Cu2+ with the limit of detection as low as 5.6 nM. The mechanism of the Cu2+ induced fluorescence quenching of a-GQDs can be attributed to the electron transfer by the formation of metal complex between Cu2+ and the amino groups on the surface of a-GQDs. These results suggest great potential for the simple and green synthesis of functionalized GQDs and a practical sensing platform for Cu2+ detection in environmental and biological applications.