We demonstrated that graphene oxide (GO) can be oxidized and cut into graphene quantum dots (GQDs) by hydroxyl radicals (˙OH), which is obtained by the catalytic decomposition of hydrogen peroxide (H2O2) with a tungsten oxide nanowire (W18O49) catalyst. The clean oxidizing agent (H2O2) and the solid catalyst lead to a simple GQD preparing method without any by-products. The obtained GQD aqueous solution can be directly applied to fluorescence imaging in vitro without any further purification. The effect of the W18O49 catalyst on the ˙OH formation is discussed, and the size of GQDs can be controlled via changing the concentration of hydroxyl radicals.