We develop a new explicit integration method for transient dynamics computation of viscoelastic materials, surpassing the stability limits of Belytschko’s widely used half-lagged velocity approximation. Based on the central difference (CD) scheme, our method integrates the viscous stress strain law, while keeping an explicit scheme. Moreover, we provide a new stability analysis of the variable time step central difference method. We prove that CD’s stability can be ensured only thanks to the zero-stability criteria, based on the multistep formulation of the method. We perform analytical developments on a single degree of freedom problem. Thus, we show that, without viscous damping, ensuring stability requires to decrease, or at least to maintain constant the time step during the time integration. Furthermore, we prove that, with viscous damping, there exists a slight possibility of increasing the time step during the time integration.