Transmission properties of transverse magnetic light through periodic sub-wavelength slit apertures on a metallic film, behind which is another planar metallic film, are studied by finite-difference-time-domain method with constant periodicity and slit width. The result shows that the transmitted energy is strongly correlated to both the thickness of the metallic grating and the distance between such two films at a specific wavelength. The thickness of the grating acts as a filter that allows specific wavelengths to go through the slits, while the distance of dual metallic film dominantly determines a constructive or destructive interference between the transmitted light through the slits and the reflected wave from the back film. Besides, a strong vibration in the transmission spectrum as a function of the grating thickness is interestingly observed, which can be interpreted by the resonance of the surface plasmons of the front and the back metallic films.