Reflection is a natural phenomenon that occurs when light passes the interface between materials with different refractive index. In many applications, such as solar cells or photodetectors, reflection is an unwanted loss process. Many ways to reduce reflection from a substrate have been investigated so far, including dielectric interference coatings, surface texturing, adiabatic index matching and scattering from plasmonic nanoparticles. Here we present an entirely new concept that suppresses the reflection of light from a silicon surface over a broad spectral range. A two-dimensional periodic array of subwavelength silicon nanocylinders designed to possess strongly substrate-coupled Mie resonances yields almost zero total reflectance over the entire spectral range from the ultraviolet to the near-infrared. This new antireflection concept relies on the strong forward scattering that occurs when a scattering structure is placed in close proximity to a high-index substrate with a high optical density of states.