In South America, the presence of the non-native mollusc Limnoperna fortunei (Dunker, 1857) (Mollusca, Bivalvia, Mytilidae) in rivers and reservoirs may result in several impacts on the environment and economic activities. In a continental scale, the factors that most influence the dispersion of the species are anthropogenic vectors such as the movement of boats and people. Due to this, distribution models based solely on climatic variables often fail to predict the areas most subject to invasion, both spatially and temporally. An alternative to overcome this problem is the evaluation assuming the phenomenon as a complex system. In this paper, we have used a cellular automata model to predict the spread of the golden mussel in the Brazilian territory, on a temporal and spatial scale. We assume three parameters of interest: a) altitude b) characteristics of the river, and c) human population density. Transition rules were defined based on various considerations discussed in the article. The algorithm estimated satisfactorily the risk of invasion by L. fortunei to date (year of 2016), and the simulations for the years 2030 and 2050 predicted a high risk of invasion in north and northeastern Brazil. The increased risk of invasion predicted by the model for the next decades indicates that prevention and control measures should be applied immediately and this is of the utmost importance for the country to be able to comply with the #9 Aichi target.