In the synchronized switching damping (SSD) techniques, the voltage on the piezoelectric element is switched synchronously with the vibration to be controlled using an inductive shunt circuit (SSDI). The inherent capacitance and the inductance in the shunt circuit comprise an electrically resonant circuit. In this study, a negative capacitance is used in the shunt circuit instead of an inductance in the traditional SSD technique. The voltage on the piezoelectric element can be effectively inverted although the equivalent circuit is capacitive and no resonance occurs. In order to investigate the principle of the new SSD method based on a negative capacitance (SSDNC), the variation of the voltage on the piezoelectric element and the current in the circuit are analyzed. Furthermore, the damping effect using the SSDNC is deduced, and the energy balance and stability of the new system are investigated analytically. The method is applied to the single-mode control and two-mode control of a composite beam, and its control performance was confirmed by the experimental results. For the first mode in single-mode control, the SSDNC is much more effective than SSDI. In other cases, the SSDNC is also more effective than the SSDI, although not significantly.