Bioinspired moth-eye surface provides broadband antireflection features, which significantly enhance performances in optical components/devices. However, their practical uses are strictly limited due to poor mechanical stability of nano-patterns. In this study, we artificially engineered moth-eye structures on polycarbonate substrate through a thin-film coating of mechanically stable dielectric materials (i.e., Al_2O_3, Cr_2O_3, ZrO_2, and TiO_2 etc). The geometry of Al_2O_3-coated moth-eye surface is designed by considering the effective medium theory and confirmed by calculation of diffraction efficiency based on a rigorous coupled-wave analysis method. The tailored Al_2O_3-coating on moth eye surface exhibit the improved hardness while maintaining high optical transmittance.