A metal-insulator-metal (MIM) waveguide with tooth cavity-coupled ring splitting cavity is proposed. Transmission characteristics and refractive index sensitivity are investigated by using finite-element method. A Fano-like line is observed in the transmission spectrum, and it is caused by the coherent superposition of the narrow discrete and wide continuous states. A maximum sensitivity of 1200nm/RIU is achieved based on the Fano resonance effect when the air in the MIM waveguide and cavity is replaced by an insulator with a different refractive index. In addition, the derived structures of the plasmonic system are studied, and multiple Fano-like resonances are observed in the transmission spectrum. The effects of the structural parameters of plasmonic system on the Fano resonance are also investigated.