A method for forming an anti-reflection coating of alkali-treated silica aerogel on a substrate, comprising the steps of hydrolyzing and polymerizing alkoxysilane in the presence of a base catalyst to prepare an alkaline sol, adding an acid catalyst to the alkaline sol to carry out further hydrolysis and polymerization to prepare a first acidic sol, hydrolyzing and polymerizing alkoxysilane in the presence of an acid catalyst to prepare a second acidic sol, mixing the first and second acidic sols, applying the resultant mixed sol to the substrate, drying it, and treating the resultant silica aerogel coating with an alkali.