In case of oxidizing cycloalkane with oxygen, the catalyst to be used is a catalyst obtained by supporting metals of Groups 5 to 10 of the Periodic Table on a carrier, the carrier being subjected to a catalytic treatment with an organosilicon compound. The metal is preferably vanadium, chromium, manganese, iron, cobalt, ruthenium or palladium, while the carrier is preferably an oxide of magnesium, aluminum, silicon, titanium or zirconium.