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Bandwidth-tunable light absorption enhancement in monolayer graphene is practically important for graphene-based photoelectric devices. Especially, it is still a huge challenge to achieve high-efficiency graphene absorption with extremely narrow sub-nanometer bandwidth much smaller than one nanometer. In this work, both broadband and narrowband absorption peaks of monolayer graphene are numerically achieved in visible and near-infrared wavelength ranges. The broadband absorption peak is ascribed to localized dipolar plasmon resonances in individual silver nanodisks, and the narrowband absorption peak arises from collective first-order diffraction coupling effect in periodic array of silver nanodisks. By changing the array period, the full width at half maximum (FWHM) of the broadband absorption peak can vary from 100 nm to 50 nm. Correspondingly, the FWHM of the narrowband absorption peak is tuned from about 6.4 nm to only 0.25 nm, thus realizing an ultra-narrow sub-nanometer bandwidth.