To limit the quantity of a vibration control member deformed within tolerance while absorbing overload by a means excepting the vibration control member when overload works to a damper.

The vibration control member 11 composed of a viscoelastic body is disposed around a cable in the vicinity of a cable fixing section 13 for the cable 3 for supporting a heavy structure. The first and second mounting plates 15, 14 are fixed at both ends of the vibration control member 11 mutually oppositely. The first mounting plate 15 is connected on the cable fixing section side, and the second mounting plate 14 is connected to the cable 3 on the reverse side to the cable fixing section 13. Stopper means 32 limiting the quantities of relative displacement in the relative shearing directions of a pair of the mounting plates 14, 15 within the tolerance of the vibration control member 11 are installed. A slip means 31 permitting slip movement in the shearing directions of the first or the second mounting plates 15, 14 under the state in which the stopper means 32 function is interposed to at least either one of a section between the first mounting plate 15 and the cable fixing section 13 or a section between the second mounting plate 14 and the cable 3.