A 3-alkenylcephem compound of the formula (1) wherein R1 is benzyl or phenoxymethyl, R2, R3 and R4 are alike or different and are each a hydrogen atom, C1-10 alkyl, C4-8 cycloalkyl or aryl C1-3 alkyl substituted or unsubstituted with C1-4 alkyl, R2 and R3, when taken together, form a group —(CH2)lXm(CH2)n— substituted or unsubstituted with C1-4 alkyl at an optional position, X is an oxygen atom or group —N(R5)—, l is 0 to 3, m is 0 or 1, n is an integer of 2 to 4, R5 is a hydrogen atom or C1-4 alkyl.