Graphics Processing Units (GPU) for General-Purpose parallel computing are applied in this work to support the construction of state-space graphs of Input-Output Place-Transition (IOPT) Petri net models (commonly known as reachability graphs). Starting from previous works already integrated and publicly available in the IOPT-Tools framework, a new algorithm to build the state-space graph is proposed based on its adaptation to General-Purpose computing on GPU platforms (GPGPU). To implement the new algorithm, part of the code that is automatically generated by the state-space generator of the IOPT tool framework was adapted to run on a NVIDIA GPU under the Compute Unified Device Architecture (CUDA) Toolkit. The GPU was used as a co-processor, namely the known sequential part of the algorithm runs on the CPU and the identified computationally-intensive part, concerning to the treatment of each unprocessed state and the calculation of all its child nodes, is handled by the GPU. A set of IOPT models already available at the IOPT-Tools framework are used to validate the results obtained with the new algorithm.