In this paper, using the surface plasmon and Fabry–Pérot (FP) cavity, the design of a symmetric silicon grating absorber is proposed. The time-domain finite difference method is used for simulation calculations. The basic unit structure is a dielectric grating composed of silicon dioxide, metal and silicon. Through the adjustment of geometric parameters, we have achieved the best of the symmetric silicon grating absorber. A narrowband absorption peak with an absorption rate greater than 99% is generated in the 3000–5000 nm optical band, and the wavelength of the absorption peak is λ = 3750 nm. The physical absorption mechanism is that silicon light generates surface plasmon waves under the interaction with incident light, and the electromagnetic field coupling of surface plasmon waves and light causes surface plasmon resonance, thereby exciting strong light response modulation. We also explore the influence of geometric parameters and polarization angle on the performance of silicon grating absorbers. Finally, we systematically study the refractive index sensitivity of these structures. These structures can be widely used in optical filtering, spectral sensing, gas detection and other fields.