This work presents a fully GPU-accelerated algorithm for the polygonal mesh generator known as Polylla. Polylla is a tri-to-polygon mesh generator, which benefits from the half-edge data structure to manage any polygonal shape. The proposed parallel algorithm introduces a novel approach to modify triangulations to get polygonal meshes using the half-edge data structure in parallel on the GPU. By changing the adjacency values of each half-edge, the algorithm accomplishes to unlink half-edges that are not used in the new polygonal mesh without the need neither removing nor allocating new memory in the GPU. The experimental results show a speedup, reaching up to ×83.2 when compared to the CPU sequential implementation. Additionally, the speedup is ×746.8 when the cost of copying the data structure from the host device and back is not included.