Abstract: It is of great importance to reduce micro-vibration e ect on precision instrument, and employing viscoelastic damper to reduce micro-vibration is an innovative and challenging issue. In this paper, the molecular chain network model is employed to analyze the viscoelastic material microstructures, and the e ect of the network chains and free chains on the viscoelastic properties of viscoelastic material is comprehensively considered, and then a mechanical model of VE damper under micro-vibration is proposed based on molecular chain structures. The standard linear solid model and Maxwell model are adopted to describe the mechanical behaviors of the single network chain and single free chain, respectively. Moreover, eight-chain network model and three-chain network model are then employed. Additionally, temperature-frequency equivalent theory is adopted to reflect the temperature e ect. The proposed model is able to describe the mechanical properties of viscoelastic damper at di erent frequencies and temperatures, and this model can reflect the material microstructure e ect on its viscoelastic properties. To verify the proposed model and reveal the mechanical behavior of viscoelastic damper under micro-vibration excitations, tests on viscoelastic damper are carried out. The results show that viscoelastic damper has good energy dissipation capacity; the dynamic properties are significantly influenced by frequency and temperature, and the proposed model can accurately describe the dynamic properties of viscoelastic damper at di erent temperatures and frequencies under micro-vibration excitations.