An alkoxylation catalyst for causing an alkylene oxide to react with an organic compound having one or more active hydrogen, comprising magnesium oxide modified by the addition of at least one metal ion selected from the group consisting of Al.sup.3+, Ga.sup.3+, In.sup.3+, Tl.sup.3+, Co.sup.3+, Sc.sup.3+, La.sup.3+, and Mn.sup.2+. In the presence of the catalyst, an addition polymerization reaction between the alkylene oxide and the organic compound having one or more active hydrogen such as an alcohol or phenol can be performed with only small amounts of unreacted material and byproducts, and the alkylene oxide adduct having a very narrow alkylene oxide adduct distribution can be obtained.