A damping structure which dispenses of the connection of a resistor used for a conventional damping structure and undergoes diverse molding processings with a simpler structure, and a laminate damping base material constituting such a damping structure. A laminate damping base material made of a piezoelectric ceramic material or piezoelectric polymer material and a conductive fiber-reinforced plastic (FRP) composition is prepared. One to a plurality of this base material are stacked to constitute a first damping structure. A second damping structure is constituted by stacking at least a layer of piezoelectric polymer film or piezoelectric ceramic thin film between a multilayer laminate that is a laminate of conductive laminate FRP base materials.