Abstract: Viscoelastic materials are extensively utilized in civil engineering, aviation, and other domains owing to their superior vibration damping characteristics. The nonlinear stiffness Zener model was employed to replace the energy transfer elements in the conventional nonlinear energy trap, thereby making a novel viscoelastic energy trap device. Furthermore, the bifurcation behavior of the model under simple harmonic excitation was investigated. Initially, the nonlinear dynamic control equation for the coupled main structureenergy trap system was formulated based on the nonlinear stiffness Zener model. Subsequently, the slowvarying system’s equation under the 1∶1 resonance condition was analytical derived with the complex variable averaging method. On this basis, the effects of key parameters on the bifurcation behavior of the system's viscoelastic energy trap under slowchanging conditions were elucidated. Through integration of the numerical simulation approach and in view of the vibration reduction efficiency and energy transfer efficiency of the main structure as evaluation indicators, the vibration suppression effectiveness of the viscoelastic energy trap across different bifurcation regions was further explored. The results indicate that, the newly developed viscoelastic energy trap can effectively modulate saddlenode bifurcations and Hopf bifurcations through parameter adjustments, thereby significantly enhancing the system’s vibration damping efficiency and energy transfer efficiency while effectively restraining the displacement response of the main structure. This research provides a robust theoretical foundation for the engineering design and parameter optimization of the innovative viscoelastic energy trap.