This paper demonstrates a new semi-active vibration control method with harmonically varying damping on a serial two-degree- of freedom system. We applied the method of the harmonically varying damping to vibration mitigation of a single-degree-of-freedom structure and a parallel-coupled structure with dual frequency sinusoidal base excitation. However, no such study considering the serial multi-degree-of-freedom system has been conducted. In this paper, the proposed semi-active control law is applied for the serial multi-degree-of-freedom system, i.e., the structures with the seismic isolation layer. To more specifically, the primary mode response of the structure is controlled by the effect between harmonically varying damping and the higher-order mode response of the structure. However, the proposed control law requires the phase of the each mode response of the structure. Therefore, a new filter using a nonlinear oscillator, Stuart-Landau equation, is also proposed. The filter harnesses the synchronization properties of nonlinear oscillators, and can separates each mode vibration to estimate the each phase. The validity of the proposed system is shown by numerical simulation.