A vinyl- or allyl-containing compound represented by following Formula (3): wherein R2, R3, R4, R5, and R6 each represent hydrogen atom or a nonmetallic atom-containing group; R7 represents a nonmetallic atom-containing group; Y represents a group selected from the group consisting of —Si(R8)(R9)—, —Si(R10)(R11)—O—, the left hand of which is combined with R7, and —NR12—, wherein R8, R9, R10, R11, and R12 each represent hydrogen atom or a nonmetallic atom-containing group; and “n” represents 0 or 1, is prepared by reacting a vinyl or allyl ester compound represented by following Formula (1): wherein R1 represents hydrogen atom or a nonmetallic atom-containing group; R2, R3, R4, R5, R6, and “n” are as defined above, with a compound represented by following Formula (2): R7—Y—H   (2) wherein R7 and Y are as defined above, in the presence of a transition element compound.