The present invention relates to a process for preparing a tris[3-(alkoxysilyl)propyl] isocyanurate from the group of tris-[3-(trialkoxysilyl)propyl] isocyanurate, tris[3-(alkyldialkoxysilyl)propyl] isocyanurate and tris[3-(dialkylalkoxysilyl)propyl] isocyanurate by hydrosilylation, by in step A initially charging a mixture comprising at least one hydroalkoxysilane from the group of hydrotrialkoxysilane, hydroalkyldialkoxysilane, hydrodialkylalkoxysilane [called H-silane(s) for short], at least one carboxylic acid and a Pt catalyst, heating the mixture to a temperature of 50 to 140° C., in step B adding a mixture of 1,3,5-triallyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione and at least one alcohol to the mixture from step A while mixing, in step C leaving the mixture from step B to react while mixing and in step D working up the product mixture thus obtained.