In this work, we present a numerical approach for simulating wave propagation in unbounded domains which combines discontinuous Galerkin methods with arbitrary high order time integration (ADER-DG) and a stabilized modification of perfectly matched layers (PML). Here, the ADER-DG method is applied to Bérenger’s formulation of PML. The instabilities caused by the original PML formulation are treated by a fractional step method that allows to monitor whether waves are damped in PML region. In grid cells where waves are amplified by the PML, the contribution of damping terms is neglected and auxiliary variables are reset. Results of 2D simulations in acoustic media with constant and discontinuous material parameters are presented to illustrate the performance of the method.