Abstract Predicting the routes of maritime traffic can improve economic efficiency, decrease ecological impact, and improve safety at sea. Over scales that are small (few hundred meters) and large (dozens to hundreds of kilometers), vessel trajectories have successfully been predicted by deep learning and (static) network-based approaches, respectively. We present an approach for medium to large scales (few kilometers) where (a) a maritime traffic network is automatically constructed from AIS messages, and (b) vessel trajectories are predicted as most likely paths through the network. Using three regions (Stavanger, Tromsø, and Oslo), we show that the network can capture up to ∼ 90 per cent of all maritime traffic (excluding pleasure craft) with a median absolute error of ∼ 80 meters. Vessel paths are sequences of waypoints and legs (nodes and edges) and are map-matched onto the network from vessel trajectories. Once mapped, we predict future paths for two subproblems – (i) known destination, and (ii) unknown destination. We use four algorithms (Dijkstra, Markov, MOGen, GRETEL). For known destinations, we find that Dijkstra performs best. In Stavanger (Tromsø, Oslo), Dijkstra predicts 64 (42, 68) per cent of path segments correctly and keeps the median path error below 15 (33 and 55) meters. For unknown destinations, performance depends on the forecast horizon (the number of legs k to predict). For k ≤ 5, Markov is best and predicts 62 (48, 72) per cent of legs correctly. For k > 5, GRETEL performs best and predicts 54 (47, 63) per cent of legs correctly. For some types of vessels, models improve by considering vessel type. For passenger vessels, models specific to them predict ∼ 10 per cent better paths with half the distance error. For tankers, paths (and distance errors) are 6 (20) per cent worse. For auxiliary vessels, path quality is unchanged, but distance error improves ∼ 36 per cent.