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 in a hot water with a temperature of 60° C. to 100° C. to form a textured structure made of aluminum oxide crystals, the aluminum oxide film being formed by feeding the precursor sol of aluminum oxide onto a base. A method for producing an optical member includes a step of immersing an aluminum oxide film in a hot water with a temperature of 60° C. to 100° C. to form a textured structure made of aluminum oxide crystals, the aluminum oxide film being formed by feeding the precursor sol of aluminum oxide onto a base.