PROBLEM TO BE SOLVED: To obtain the subject compound having γ-selectivity without being accompanied with the production of a telomere by the acid-catalyst condensation reaction of an acetylated polyene aldehyde with a vinyl ketene acetal. SOLUTION: A polyene (di)O,O-dialkylacetal of the formula: A-CH(OR )2 (A is a monovalent conjugated polyene; R is a 1-6C alkyl) or the formula: (R O)2 HC-B-CH(OR )2 (B is a divalent conjugated polyene) is reacted with a vinyl ketene acetal or formula I (R , R are each H, CH3 ; R is a 1-6C alkyl; R is a 1-6C alkyl, etc.,) or its analog in the presence of a Lewis acid and subsequently removing the δ-positioned alkanol from the reaction product under a basic condition to obtain the polyenoic acid ester or polyenoic acid of formula II (R is H a 1-6C alkyl, etc.,) or formula III. The method thereby has advantageous points such as an advantageous point that the reaction is exclusively generated at the γ-position of the vinyl ketene acetal derivative.