We investigate theoretically the electromagnetic propagation properties of graphene plasmons in a comb-like dielectric-graphene-dielectric (DGD) waveguide. The effective index of surface plasmon mode supported by the waveguide is analysed numerically, and it is found that the effective refractive index increases with the refractive index of the dielectric and decreases with Fermi energy of the graphene sheet. For a comb-like DGD waveguide with a finite branch length, a subwavelength plasmon filter can be formed by Fabry-Perot resonance caused by the reflection of the guided mode at the branch. The central frequencies of the gaps can be changed by varying the length of the branch, Fermi energy, the refractive index of the dielectric and the layer number of graphene sheets. The analytic and simulated result reveals that a novel nanometric plasmonic filter in such a comb-shaped waveguide can be realized with ultracompact size in a length of a few hundred nanometers in the mid-infrared range. We find that the frequencies of the stopband increase with Fermi energy and the layer number of graphene sheets, while will they decrease nonlinearly with the length of the branch and the refractive index of the dielectric. In addition, the width of the gap can be increased with the number of comb branches. Such electromagnetic properties could be utilized to develop ultracompact photonic filters for high integration.