ZN-37 special damping silicone rubber is a viscous damping material capable of dissipating and storing vibrational energy，and is widely used in high-precsion vibration damping structures in aerospace and other fields.When analyzing and designing vibration reduction structures based on ZN-37 special damping silicone rubber，it is particularly crucial to fully characterize the viscoelastic mechanical behavior of the material and accurately describe its constitutive relationship.Based on the Zener modified model， the visco-hyperelastic constitutive model of ZN-37 special damping silicone rubber is decomposed into a parallel coupling system of the hyperelastic constitutive model and the viscoelastic constitutive model.Material parameters for the constitutive model are obtained through quasi-static tensile tests and stress relaxation tests on standard specimens.The reliability of the constitutive model is verified using quasi-static tensile tests conducted at different loading rates.The established visco-hyperelastic constitutive model can effectively reflect the mechanical properties of ZN-37 special damping silicone rubber at low loading rates.