To harness the full spectrum of solar energy, Fresnel reflection at the surface of a solar cell must be eliminated over the entire solar spectrum and at all angles. Here, we show that a multilayer nanostructure having a graded-index profile, as predicted by theory [J. Opt. Soc. Am. 66, 515 (1976); Appl. Opt. 46, 6533 (2007)], can accomplish a near-perfect transmission of all-color of sunlight. An ultralow total reflectance of 1%-6% has been achieved over a broad spectrum, lambda = 400 to 1600 nm, and a wide range of angles of incidence, theta = 0 degrees-60 degrees . The measured angle- and wavelength-averaged total reflectance of 3.79% is the smallest ever reported in the literature, to our knowledge.