A graphene-metamaterial composite photodetectors with graphene embedded in metamaterial perfect absorbers (MPAs) is proposed and their light absorption properties are numerically investigated. Absorption above 40% in graphene monolayer is obtained due to the strongly localized electromagnetic resonance and the suppression of reflection and transmission loss in MPAs. The working frequency of the graphene photodetector can be tunable and deter- mined by MPAs due to the ultrabroad absorption band of graphene. The novel idea of using MPAs to enhance the interaction between light and graphene could be also adopted in other graphene optoelectronic devices.