In this paper, a novel structure of photodetector consisting of periodic layers of graphene and silica located on a metal film with groove rings of silica is proposed. The excited localized Plasmon resonance in groove rings makes a strong enhancement of  light absorption in the graphene layer. The numerical results revealed that the graphene absorption  increases from 2.3% to %47.5 and even in three-layer graphene, increases up to a maximum value of %80.7 in the C band. In addition, the absorption peak is dependent on the groove depth and ring radius as well as the number of graphene layers. Also, a photoresponsivity of 100A/W and photocurrent of 50mA at -1.5V bias and at wavelength of 1.55µm are achieved.