The extraordinary optical transmission properties of periodic subwavelength hole arrays were of great significance in the design of subwavelength optoelectronic devices. The periodic hole array structure on two or more layers can lead to new optical properties due to the interaction of the electromagnetic fields between the layers. The transmission properties of a rectangular nanohole array in Au-dielectric-Au multilayer films were simulated using the finite-difference time-domain method. The results show that there are multiple transmission peaks in the transmission spectra of the structure in the near-infrared region.The number, position and intensity of the transmission peak can be controlled by changing the geometrical parameters of the structure and the dielectric film of material. The influences of the thickness and refractive index of the dielectric film, the period of the hole arrays, the length of the rectangular hole on the transmission spectrum were analyzed in detail. It provides a reference for designing multi-wavelength control devices using multiple surface plasmon resonances.