In this study, we design a metal-dielectric-metal (MDM) waveguide side-coupled square ring resonator with a rectangular-groove (RG). Its effective length is accurately derived through the F-P theory and a tunable multimode plasmonic filter is realized based on this structure. Based on numerical calculations and theoretical analysis, the extra non-integer resonant modes are obtained beyond the conventional integer modes. The wavelength of each non-integer resonant mode red-shifts with the increase of the RG's length because RG has the maximal effect on the magnetic field when it is located at antinodes of the magnetic fields. However, the integer modes are not sensitive to RG and their wavelengths are fixed because RG has the minimal effect on the magnetic field when it is placed on the nodes of the magnetic fields. The number of modes and their field distributions can be adjusted by changing the shape, position, and number of RGs. Compared with the conventional resonators, the proposed structure and the corresponding results are extremely useful for the design of optoelectronic devices as they can provide more channels to flexibly manipulate the resonant wavelengths.