Abstract: Based on two dimensional viscoelastic differential constitutive relationships, the differential equation of motion of a moving viscoelastic plate constituted by Kelvin-Voigt model under the action of uniformly distributed tangential follower forces is established, and the complex characteristic equation for the moving viscoelastic plate with four edges simply supported and subjected to follower forces is derived by the normalized power series method. The variation relationship between the first three complex frequencies of the system and the dimensionless moving speed, delay time as well as follower force is analyzed. The numerical results show that the dimensionless delay time, moving speed and follower force have remarkable effects on dynamic behaviors and stability of the moving non-conservative viscoelastic plate.