Based on the eigenvalue equation and finite-difference time-domain (FDTD) algorithm, the surface plasmon resonance sensing characteristics of rhombic gold nanoparticle arrays embedded in silica substrate are investigated, and relationship between the resonance mode and embedded depth is derived. The calculated results agree with the numerical simulation, which shows that the asymmetry of the upper and lower media of gold nanoparticle arrays can be equivalent to monolayer dielectric grating. The physical mechanism and influence factors of generating multiple resonance peaks in the transmission spectra are analyzed theoretically. Relationships between the transmission spectrum and embedded depth, axial ratio, array period are further discussed. The sensing performance of array structure is analyzed. It provides a theoretical basis for the fabrication of multi-band surface plasmon resonance(SPR) sensor substrate.