The human-mediated translocation of species poses a distinct threat to nature, human health, and economy. Although existing models calculate the invasion probability of any species, frameworks for species-specific forecasts are still missing. Here, we developed a model approach using global ship movements and environmental conditions to simulate the successive global spread of marine alien species that allows predicting the identity of those species likely to arrive next in a given habitat. In a first step, we simulated the historical stepping-stone spreading dynamics of 40 marine alien species and compared predicted and observed alien species ranges. With an accuracy of 77%, the model correctly predicted the presence/absence of an alien species in an ecoregion. Spreading dynamics followed a common pattern with an initial invasion of most suitable habitats worldwide and a subsequent spread into neighboring habitats. In a second step, we used the reported distribution of 97 marine algal species with a known invasion history, and six species causing harmful algal blooms, to determine the ecoregions most likely to be invaded next under climate warming. Cluster analysis revealed that species can be classified according to three characteristic spreading profiles: emerging species, high-risk species, and widespread species. For the North Sea, the model predictions could be confirmed because two of the predicted high-risk species have recently invaded the North Sea. This study highlights that even simple models considering only shipping intensities and habitat matches are able to correctly predict the identity of the next invading marine species.