This work investigates dynamic stability in transverse parametric vibration of an axially accelerating viscoelastic tensioned beam. The material of the beam is described by the Kelvin model. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a infinite set of ordinary-differential equations under the fixed–fixed boundary conditions. The method of averaging is employ to analyze the dynamic stability of the 2-term truncated system. The stability conditions are presented and confirmed by numerical simulations in the case of subharmonic and combination resonance. Numerical examples demonstrate the effects of the dynamic viscosity, the mean axial speed and the tension on the stability conditions.