Based on the transmission characteristics of surface plasmon polaritons and the optical properties of periodic photonic crystals, a hybrid structure of sub-wavelength dielectric grating-metal Ag thin film-periodic photonic crystal is proposed, which produces discrete state in sub-wavelength dielectric grating-metal Ag thin film structure and continuous state in periodic photonic crystal structure. Through the theoretical analysis and transmission characteristics of the structure, the generation mechanism of Fano resonance in the structure is expounded, the Fano-resonance sensing structure model based on angle modulation is established, and the influence of the structural parameters on the reflection spectrum curve is quantitatively analyzed. Results show that when the periodic photonic crystal periodic layer number is N=4, the grating period is Λ=258 nm, and the Ag-film thickness is d0=27 nm, the quality factor FOM value of the structure can be as high as 2.11×10 4, and the angular sensitivity is S=40 (°)/RIU. The proposed structure provides an effective theoretical reference for achieving Fano resonance in a sub-wavelength dielectric grating structure, and it has certain guiding significance to the design of the optical refractive index sensing structure.