The transverse vibration of an axially moving viscoelastic sandwich beam with small deflection was investigated. Based on the Kelvin differential constitutive equation, the transverse controlling equation was established. The eigenfunctions of the axially moving viscoelastic sandwich beam with simple supported boundary condition were obtained by using Galerkin truncation and complex mode analysis. The influence of the ratio of the core layer, axially moving velocity and axial tension on the natural frequencies and critical velocity were discussed by using numerical method.