A refractive index sensor with a composite structure based on dielectric grating with metal films is designed. The surface plasmas in the composite structure are excited by the transverse magnetic polarized light with a wavelength of 632.8 nm from a He-Ne laser and the refractive index sensor with a high sensitivity is obtained. With the finite element method, the reflection spectra for the analyte with different refractive indexes, grating thicknesses, and periods are numerically simulated. A grating thickness of 100 nm and a grating period of 500 nm are selected as the optimal parameters after the parameter optimization for the composite structure with a duty cycle of 0.5 and a metal film thickness of 45 nm. The variation of the resonance angle of the interface between the metal film and the analyte with different refractive indexes is calculated under the optimal parameters, and an angular sensitivity of 500 (°)/RIU is obtained. This refractive index sensor possesses the advantages of simple operation, low cost, and high angular sensitivity, which has considerable application prospects.