A method for producing aluminum oxide is provided. The method uses an aluminum-oxide-forming agent containing a partially hydrolyzed aluminum alkyl compound containing an aluminum trialkyl or a mixture thereof, and a solvent. It is thus possible to produce an aluminum oxide thin film or aluminum oxide particles on or in a substrate that is not resistant to polar solvents. A method of producing a polyolefin-based polymer nanocomposite containing zinc oxide particles or aluminum oxide particles using a solution containing a partially hydrolyzed zinc alkyl or a solution containing a partially hydrolyzed aluminum alkyl is also provided. The polyolefin-based polymer nanocomposite contains a polyolefin substrate and zinc oxide particles or aluminum oxide particles, and does not contain a dispersant. The zinc oxide particles or aluminum oxide particles have an average particle size of less than 100 nm.