Optical diode-like effect has sparked growing interest in recent years due to its potential applications in integrated photonic systems. In this paper, we propose and numerically demonstrate a new type of easy-processing metal/dielectric cylinder composite grating on semi-sphere substrate, which can achieve high-contrast asymmetric transmission of unpolarized light for the sum of all diffraction modes in the entire visible region, and effectively guide the diffraction light transmitting out the substrate. The asymmetric light transmission (ALT) ratio is larger than 2 dB in the waveband from 380 nm to 780 nm and the maximum ALT ratio can reach to 13 dB at specified wavelengths. The thorough theoretical research reveals that the proposed metal/dielectric pillar composite grating structure, together with the substrate, can effectively excite localized surface plasmonic resonance (LSPR) effect and waveguide mode (WGM), and enlarge the diffraction difference between forward and backward transmission spaces, including both number of diffraction orders and diffraction efficiency, thus resulting in high-contrast broadband ALT phenomenon. In particular, lowering the symmetry of the grating can achieve polarization-dependent ALT. Such a type of easy-processing ALT device with high performance for both polarized and unpolarized light can be regarded as suitable candidates in practical applications.