The type species, H. insignis, was originally described by Johann Andreas Wagner in 1860 from the Upper Jurassic plattenkalk limestones of Bavaria, Germany, and placed into the new genus Hypsocormus by Wagner in a posthumous publication in 1863.

[1] A second valid species, Hypsocormus posterodorsalis was named by Maxwell and colleagues in 2020 from the same deposits.

The species "Hypsocormus macrodon" Wagner 1863 from the Upper Jurassic of Germany has been moved to a separate genus and renamed Simocormus macrolepidotus.

[1] Hypsocormus was a fast-swimming predatory fish about 1 metre (3.3 ft) long, with a half moon-shaped caudal fin similar to that of a modern mackerel.

Its jaws were muscular and highly developed, giving it a powerful bite.