The relationship of the three living groups of sarcopterygians or lobe-finned fish (tetrapods, lungfish and coelacanths) has been a matter of debate. Although opinions still differ, most recent phylogenies suggest that tetrapods are more closely related to lungfish than to coelacanths. However, no previously known fossil taxon exhibits a concrete character combination approximating the condition expected in the last common ancestor of tetrapods and lungfish -- and it is still poorly understood how early sarcopterygians diverged into the tetrapod lineage (Tetrapodomorpha) and the lungfish lineage (Dipnomorpha). Here we describe a fossil sarcopterygian fish, Styloichthys changae gen. et sp. nov., that possesses an eyestalk and which exhibits the character combination expected in a stem group close to the last common ancestor of tetrapods and lungfish. Styloichthys from the Lower Devonian of China bridges the morphological gap between stem-group sarcopterygians (Psarolepis and Achoania) and basal tetrapodomorphs/basal dipnomorphs. It provides information that will help in the study of the relationship of early sarcopterygians, and which will also help to resolve the tetrapod-lungfish divergence into a documented sequence of character acquisition.