This paper presents a nanometer-sized metallic film periodically pierced by narrow slits with ellipse walls deposited on a substrate that demonstrates special optical properties of broadband extraordinary optical transmission (BEOT). Compared to slits with straight walls, the metal slits with nonlinearly tapered ellipse walls can collect more light on the upper surface, which is coupled into a gap plasmon polariton propagating along the ellipse walls, then delivers the light at the smaller exit slit opening. In the visible spectral region, BEOT of TM-polarized light is achieved with up to 80% transmission at resonance, which is resulted from the simultaneous enhancement of zero-order slit resonance and higher-order slit resonances excited due to the existence of the substrate. The spectral range of BEOT is limited by Wood-Rayleigh anomalies and surface plasmon polariton resonances (SPPs). The BEOT spectrum of oblique incidence with small incident angle that is divided into two separate bands are also presented and analyzed theoretically. This metallic grating overcomes the low optical transmission limit of the structures with wavelength-sized grating period in visible and near-IR regions. It can be used to design nanostructured BEOT polarizer, which is an important component in novel biomimetic-based optoelectronic systems especially those in skylight polarized environment.