The simulation of nanoscale 2D DG-MOSFETs and similar semiconductor devices through a de-terministic and accurate model can be very useful for the industry but is particularly costly from the computational point of view. In this paper, we develop a hybrid parallel solver: the computing phases which corresponds to the simulation of the Boltzmann transport equation in the longitudinal dimension are performed on the GPU, while that phases related to the modelling of the electrons as waves in the transversal dimension are computed on the multi-core CPUs by using OpenMP. We have adapted the most costly computing phases to GPU in an efficient manner, achieving high performance and reducing drastically the simulation time. We give details about the parallel-design strategy and show the performance results.