Placoderms are a diverse group of armoured fishes that dominated the aquatic ecosystems of the Devonian Period, 415-360 million years ago. The bladed jaws of predators such as Dunkleosteus suggest that these animals were the first vertebrates to use rapid mouth opening and a powerful bite to capture and fragment evasive prey items prior to ingestion. Here, we develop a biomechanical model of force and motion during feeding in Dunkleosteus terrelli that reveals a highly kinetic skull driven by a unique four-bar linkage mechanism. The linkage system has a high-speed transmission for jaw opening, producing a rapid expansion phase similar to modern fishes that use suction during prey capture. Jaw closing muscles power an extraordinarily strong bite, with an estimated maximal bite force of over 4400 N at the jaw tip and more than 5300 N at the rear dental plates, for a large individual (6 m in total length). This bite force capability is the greatest of all living or fossil fishes and is among the most powerful bites in animals.