Disclosed is a structural vibration damping device, which comprises a piezoelectric element adapted to be mounted on a structure, a shunt circuit inserted between two electrodes of the piezoelectric element, and an electric circuit for selectively opening and closing the shunt circuit. In this damping device, the electric circuit is operable, when a voltage between the electrodes of the piezoelectric element has a positive or negative extreme value due to a vibration of the structure, to close the shunt circuit so as to allow a current to flow between the electrodes of the piezoelectric element, and, when the current is reduced to zero, to open the shunt circuit so as to preclude the current flow until a voltage between the electrodes of the piezoelectric element subsequently has the extreme value. Further, each of the shunt circuit and the electric circuit is designed to be operated using only a power generated by the piezoelectric element. The damping device of the present invention makes it possible to achieve high-performance power-free damping with enhanced reliability and maintainability.