A plasmonic band-pass filter based on graphene rectangular ring resonator with double narrow gaps is proposed and numerically investigated by finite-difference time-domain (FDTD) simulations. For the filter with or without gaps, the resonant frequencies can be effectively adjusted by changing the width of the graphene nanoribbon, the coupling distance and chemical potential of graphene. In addition, by introducing narrow gaps in the rectangular ring resonators, it shows the single frequency filtering effect. Moreover, the structure also shows high sensitivity fordifferent surrounding mediums. This work provides a novel method for designing all-optical integrated components in optical communication.