To obtain the subject alcohol useful as a raw material for producing perfumes, medicines, agrochemicals, etc., industrially and advantageously, by bringing a specific compound into contact with γ-alumina in a vapor phase in a prescribed temperature range.

A compound of formula I (R1 to R6, X and Y are each H, an alkyl, etc.) (e.g. 3-methyl-1,3-butanediol) is supplied to a container charged with γ-alumina having preferably 100 m2/g-250 m2/g specific surface area at the rate of 0.1-50 g/hr based on 1 cm3 of γ-alumina, subjected to a catalytic reaction in a vapor phase at 140-250°C and a product of formula II (one of A1 and A3 is H and the other forms a C-C bond with A2) (e.g. 3-methyl-3-buten-1- ol) is continuously taken out to give the objective alcohol.