Full width at half maximum (FWHM) is an important factor affecting the performance of the sensor. In order to improve the quality factor of the surface plasmon resonance sensor, a grating-assisted ultra-narrow band multispectral plasmon resonance sensor structure is proposed in this paper. The structure is composed of periodically alternating SiO₂ and Au rectangular nanorods and is placed on the SiO₂/Al₂O₃ thin film layer. The full vector finite element method is used to simulate the optical transmission and sensing characteristics, and the effects of structural parameters and polarization state of incident light on FWHM and sensing characteristics are analyzed. The simulation results show that in the wavelength range of 800-1100 nm, there are two dips formed by plasma resonance and dielectric grating in the transmission spectrum of the structure. The corresponding FWHM can reach 0.35 nm and 0.59 nm, respectively. The refractive index sensitivity is 525.7 nm /RIU and 475.7 nm /RIU, respectively. The figure of merit is 1502.00 RIU^-1 and 806.27 RIU^-1, respectively, which had potential applications in biological detection, drug screening, membrane biology and other fields.