General Purpose Graphical Processing Units (GPUs) are affordable multi-core platforms, providing access to large number of cores, but at the price of a complex architecture with non-trivial synchronization and communication costs. This paper presents the design and implementation of a conflict-driven ASP solver, that is capable of exploiting the parallelism offered by GPUs. The proposed system builds on the notion of ASP computation, that avoids the generation of unfounded sets, enhanced by conflict analysis and learning. The proposed system uses the CPU exclusively for input and output, in order to reduce the negative impact of the expensive data transfers between the CPU and the GPU. All the solving components, i.e., the management of nogoods, the search strategy, backjumping, the search heuristics, conflict analysis and learning, and unit propagation, are performed on the GPU, by exploiting Single Instruction Multiple Threads (SIMT) parallelism. The preliminary experimental results confirm the feasibility and scalability of the approach, and the potential to enhance performance of ASP solvers.