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The growth of Ge quantum dots (QDs) using the ion beam sputtering deposition technique has been successfully conducted directly on single-layer graphene supported by SiO2/Si substrate. The results show that the morphology and size of Ge QDs on graphene can be modulated by tuning the Ge coverage. Charge transfer behavior, i.e. doping effect in graphene has been demonstrated at the interface of Ge/graphene. Compared with that of traditional Ge dots grown on Si substrate, the positions of both corresponding photoluminescence (PL) peaks of Ge QDs/graphene hybrid structure undergo a large red-shift, which can probably be attributed to the lack of atomic intermixing and the existence of surface states in this hybrid material. According to first-principles calculations, the Ge growth on the graphene should follow the so-called Volmer-Weber mode instead of the Stranski-Krastanow one which is observed generally in the traditional Ge QDs/Si system. The calculations also suggest that the interaction between Ge and graphene layer can be enhanced with the decrease of the Ge coverage. Our results may supply a prototype for fabricating novel optoelectronic devices based on a QDs/graphene hybrid nanostructure.