A precursor sol of aluminum oxide contains a polycondensate formed by the hydrolysis of an aluminum alkoxide or an aluminum salt, a solvent, and an organic aluminum compound having a specific structure. An optical member is produced by a process including a step of immersing an aluminum oxide film (3) in a hot water with a temperature of 60°C to 100°C to form a textured structure (5) made of aluminum oxide crystals, the aluminum oxide film (3) being formed by feeding the precursor sol of aluminum oxide (2) onto a base (1). A method for producing an optical member includes a step of immersing an aluminum oxide film (3) in a hot water with a temperature of 60°C to 100°C to form a textured structure (5) made of aluminum oxide crystals, the aluminum oxide film (3) being formed by feeding the precursor sol of aluminum oxide (2) onto a base (1) .