Caulophryne polynema is a species of marine ray-finned fish belonging to the family Caulophrynidae, the fanfins.

Caulophryne polynema was first formally described in 1930 by the English ichthyologist Charles Tate Regan with its type locality given as off Funchal Bay on Madeira in the eastern Atlantic Ocean.

The 5th edition of Fishes of the World classifies the Caulophrynidae within the suborder Ceratioidei of the order Lophiiformes, the anglerfishes.

Its use may date as far back as Aristotle and Cicero, who referred to anglerfishes as "fishing-frogs" and "sea-frogs", respectively, possibly because of their resemblance to frogs and toads.

The sensory cells of the lateral line system are at the tips of the filamentous rays of the dorsal and anal fins.

[7] Caulophryne polynema is found in the Atlantic Ocean from Florida in the west to Madeira in the east and as far south as Cape Verdeand as far north as Iceland.

[1] Caulophryne polynema is a predatory species in which the females lure prey into range with the esca and illicium.