This paper presents the parallel implementation, using the Compute Unified Device Architecture (CUDA) architecture, of the SCIARA-fv3 Complex Cellular Automata model for simulating lava flows. The computational model is based on a Bingham-like rheology and both flow velocity and the physical time corresponding to a computational step have been made explicit. The parallelization design has involved, among other issues, the application of strategies that can avoid incorrect computation results due to race conditions and achieving the best performance and occupancy of the underlying available hardware. Two hardware types were adopted for testing different versions of the CUDA implementations of the SCIARA-fv3 model, namely the GTX 580 and GTX 680 graphic processors. Despite its computational complexity, carried out experiments of the model parallelization have shown significant performance improvements, confirming that graphic hardware can represent a valid solution for the implementation of Cellular Automata models.