Answer Set Programming (ASP) has become the paradigm of choice in the field of logic programming and non-monotonic reasoning. With the design of new and efficient solvers, ASP has been successfully adopted in a wide range of application domains. Recently, with the advent of GPU Computing, which allowed the use of modern parallel Graphical Processing Units (GPUs) for general-purpose computing, new opportunities for accelerating ASP computation has arisen. In this paper, we describe a new approach for solving ASP that exploits the parallelism provided by GPUs. The design of a GPU-based solver poses various challenges due to the peculiarities of GPU in terms of both programmability and architecture capabilities with respect to the intrinsic nature of the satisfiability problems, which exposes poor parallelism.