
Dorset County Council has bought the skull, which is 2.4m long, and is thought to be one of the largest of its kind ever found.
Pliosaurs were a type of plesiosaur, a form of gigantic marine reptile that lived at the same time as the dinosaurs.
The Jurassic Coast covers some 150km (95 mile) stretch of coastline stretching between Dorset and East Devon and spanning 185 million years of past history.
The exact location of where the pliosaur skull was discovered is not being made public.