To provide a new vibration-resistant support structure simply formed and capable of effectively reducing the deterioration of the state of vibration of a member to be damped resulting from the resonance phenomenon of a vibration system formed of a separate member such as a sub frame without requiring a complicated control type vibration-resistant mount.

The separate member 14 is supported on the member 12 to be damped to prevent vibration. An additional mass body 26 is installed separately from the separate member 14 so that the mass of the additional mass body 26 allowed to act on the separate member 14 can be changed over by a selective connection means 30.