The non-resonant extraordinary optical transmission (EOT) can achieve broadband transmission, which is significant for broadband light harvesting devices. A metallic single slit nanostructure or slit array structure, due to simple structure and easy-to integration, has been used to construct a light source in the nanostructures based on the surface plasmon polaritons (SPPs). To obtain broadband transmission, in this paper, we propose a sandwich-shaped multilayer tapered metallic slit arrays. The transmission properties of the multilayer tapered metallic slit arrays were investigated using the finite element method (FEM). Results show that, compared with monolayer tapered metallic slit arrays structure, multilayer tapered metallic slit arrays can achieve more transmission peaks in the spectra and leading to broadband transmission in the infrared; the tapered provides a gradual impedance variation from the entrance to the exit of the slits, the light is strongly localized and enhanced at the slit exits and the dielectric layer, in contrast with straight slits. In addition, the effects of the thickness of the dielectric layer, the position of dielectric layer, the period of the arrays and the width of the slit entrance on the transmission property were also studied. These results would be helpful for designing the broadband transmission properties of multilayer structures and may be applied value in the fields of nano-light source design, photonic integrated circuits and optoelectronic circuits and so on.