A class of single tooth-shaped plasmonic filter based on graphene nanoribbon is proposed in this paper, and the structure is numerically analysed by using finite-difference time-domain method. The tooth-shaped structure of graphene nanoribbon can induce a sharp band-stop effect in the transmission spectrum, and the filtering characteristics can be analysed by the scattering matrix method. The effective refractive index of the plasmonic waveguide mode in the graphene nanoribbon is analysed numerically, and it is found that the effective refractive index is influenced by both the chemical potential and the width of the nanoribbon, and when the width is narrower than 30 nm, the higher order mode disappears and the ribbon becomes a single mode waveguide. According to the scattering matrix method, the central frequencies of the transmission dips can be changed by changing the length and the width of the tooth. Flexible electrical tunability of this kind of filter by tiny change of the chemical potential of the graphene through electrical gating is also validated. In addition, transmission spectrum of multi-teeth shaped plasmonic filter is also studied. This kind of structure can possess the broad band-stop filtering property. The influences of tooth number and tooth period on transmission spectrum are investigated. We find that the transmission value can be reduced down to almost zero by adjusting the number of the teeth, also the tooth period can influence the central frequency of the stop band because of the coupling effects between each other. Like the single-tooth filter based on graphene nanoribbon, the multi-tooth broad band-stop filter can also be flexibly tuned by the geometric parameters of the structure and the chemical potential of the graphene. This work provides an effective method of designing graphene based ultra-compact tunable devices, and has extensive potential for designing all-optical integrated architectures for optical networks, communication and computing devices.