To study the bandgap coupling mechanism between nonlinear synchronized switch damping and multi-order linear resonant bandgaps, this research investigates the bandgap coupling effects between nonlinear synchronized switch damping and two-order linear resonant bandgaps in a piezoelectric meta-structure. Specifically, a piezoelectric meta-structure with hybrid nonlinear synchronized switch damping and linear two-order linear resonant electrical networks is proposed. Based on the theoretical modeling of the proposed structure, band structure and vibration transmittance performance are investigated in detail. Results showed that bandgap coupling can produce a trade-off with the advantages of both nonlinear and two-order linear resonant bandgaps. The new bandgap can not only realize broadband wave attenuation performance but also greatly enhance the attenuation in selected frequency bands, which provides a new method to manipulate elastic waves in a diversified way.