Pre-stretch affects the dynamic performance of the dielectric elastomers (DEs). In this paper, the effects of pre-stretch on the nonlinear viscoelastic oscillation and stability of the DE membrane actuator are investigated. Analytical model based on Euler-Lagrange method and homogeneity assumption is developed to describe the complex dynamic behaviour of the viscoelastic DE membrane actuator under equibiaxial and non-equibiaxial pre-stretches, respectively. Numerical calculations are applied to predict dynamic responses of the DE membrane actuator with different initial stretch ratios. The results indicate that the viscoelastic creep of the DE membrane actuator can be eliminated by specific initial stretch ratio. The phase paths and Poincaré maps reveal that proper pre-stretch helps to improve the stability of the DE membrane actuator. This work provides guidance for the structure design, stability control, and optimization of soft actuators and soft robots.