The accelerated molecular dynamics (aMD) method has recently been shown to enhance the sampling of biomolecules in molecular dynamics (MD) simulations, often by several orders of magnitude. Here, we describe an implementation of the aMD method for the OpenMM application layer that takes full advantage of graphics processing units (GPUs) computing. The aMD method is shown to work in combination with the AMOEBA polarizable force field (AMOEBA-aMD), allowing the simulation of long time-scale events with a polarizable force field. Benchmarks are provided to show that the AMOEBA-aMD method is efficiently implemented and produces accurate results in its standard parametrization. For the BPTI protein, we demonstrate that the protein structure described with AMOEBA remains stable even on the extended time scales accessed at high levels of accelerations. For the DNA repair metalloenzyme endonuclease IV, we show that the use of the AMOEBA force field is a significant improvement over fixed charged models for describing the enzyme active-site. The new AMOEBA-aMD method is publicly available (http://wiki.simtk.org/openmm/VirtualRepository) and promises to be interesting for studying complex systems that can benefit from both the use of a polarizable force field and enhanced sampling.