Asymmetric transmission phenomenon has attracted tremendous research interest due to its potential applications in integrated photonic systems. Broadband asymmetric transmission (BAT) is a highly desirable but challenging functionality to achieve in the visible regime due to the limitation of material dispersion. In this paper, we propose and numerically demonstrate that a tapered-metal-grating structure (TMGS) can achieve high-contrast BAT spectra covering the entire visible region. The transmission efficiency reaches ~95% for the forward illumination and ~35% for the backward illumination at the same wavelengths, respectively, and the corresponding transmission ratio is larger than 2.5 over a broadband wavelength regime. Such a design with high performance suggests applications for unidirectional optical transmission, optical diode, and so on.