The bandwidth-tunable absorption enhancement of monolayer graphene is theoretically studied in the near-infrared wavelengths. The monolayer graphene is placed on the silver substrate surface with a periodic array of one-dimensional slits. Two absorption peaks are found to result from the hybridization of delocalized surface plasmon polaritons and localized magnetic plasmons. The positions of absorption peaks are accurately predicted by a coupling model of double oscillators. The full width at half maximum of absorption peaks is largely tuned from about 1-200 nm by changing the array period of slits. The effect of the slit size on absorption peaks is also investigated in detail. Our work is promising in applications for photoelectric devices.