In this paper, a multichannel refractive index sensor based on a subwavelength metal–insulator–metal (MIM) waveguide coupled with tangent-ring resonators is proposed. When two tangent-ring resonators were placed above the MIM waveguide, Fano resonance with asymmetrical line shape appeared in the transmission spectrum due to the interference between the light–dark resonant modes. The sensitivity and figure of merit were as high as 880 nm/RIU and 964, respectively. Through adding more tangent-ring resonators, multiple Fano resonances with ultrasharp peaks/dips were achieved in the wavelength range of 800–2000 nm. Besides, negative group delays were also observed in the Fano resonant dips. Two-dimensional finite-difference time-domain (FDTD) method was used to simulate and analyze the performances of the proposed structures. These kinds of multiring structures can find important applications in the on-chip optical sensing and optical communication areas.