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 of general formula (1): wherein R1 and R2 each represent an alkyl group having 1 to 6 carbon atoms, a perfluoroalkyl group, or an allyl group; R3 represents an alkyl group having 1 to 6 carbon atoms, a perfluoroalkyl group, an allyl group, or an aryl group; and n represents an integer of 1 to 3. 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.