A vibration damping structure includes a panel which is a structure and a damping member joined to the panel. The damping member has a plurality of joined portions joined to a mating surface of the panel through respective joined surfaces in the X direction, and a plurality of spacing portions recessed toward the side opposite to the panel in the Z direction between adjacent joined portions. The damping member is formed such that the damping member is higher in damping than the panel and a resonance frequency of the damping member is formed such that it is substantially the same as a primary resonance frequency of the panel.