In a method for forming an abrasion-resistant coating film by heat-curing a coating composition composed mainly of a partially hydrolyzed product of alkoxysilane represented by the formula:R.sub.n.sup.4 Si(OR.sup.5).sub.4-nwherein n is an integer of 0 to 2; R.sup.4 is alkyl having 1 to 6 carbon atoms, phenyl, allyl, vinyl, methacryloxy, methacryloxyalkyl, mercaptoalkyl, aminoalkyl, epoxyalkyl, epoxyalkyloxy, epoxyalkyloxyalkyl, tetrahydrofuryl or fluoroalkyl; and R.sup.5 is alkyl having 1 to 4 carbon atoms, an improvement comprises using as a curing catalyst one or more compounds selected from the group consisting of alkali metal salts of thio-acid, dithio-acid and their derivatives; barbituric acid and its derivatives; and .beta.-dicarbonyl compound.