Abstract: Based on the theory of small deflection of thin plate and the constitutive description of Kelvin-Viogt viscoelastic material, the controlling equation which dominates the transverse vibration of the axially moving viscoelastic sandwich plate was established, followed by the study of the transverse vibration characteristic. One-mode and two-mode eigenequation were obtained by using 1-term and 2-term Galerkin truncation. The influence of the ratio of the core and axially moving velocity on the transverse vibration characteristic was discussed. It is found that both 1-term and 2-term Galerkin truncation results fit well when the axially moving velocity doesn't exceed the critical velocity. However, 1-term Galerkin truncation will not suit any more when the axially moving velocity exceeds the critical velocity. For simply supported plate at four sides, the critical velocity and coupled mode flutter velocity increase with the decrease of ratio of core.