The eel catfish, Channallabes apus, is found in the muddy swamps of the tropics of western Africa.
The 30-40cm-long (12-16in) fish is able to propel itself out of the water and bend its head downwards to capture insects in its jaws.
The Belgian researchers, writing in the journal Nature, hope this discovery will help to explain how fish moved from sea to land millions of years ago.
With a small head and a long, flexible body, C. apus has an eel-like appearance. The fish's diet provided the scientists with the first clue to its remarkable behaviour - it mainly eats beetles which are found on land.
After an expedition to study the fish in its swampy habitat in Gabon, Africa, the team brought some of the animals back to Belgium for further research.
They placed the fish in a specially designed aquarium with both wet and muddy areas, mimicking C. apus's natural environment.
"We pointed high-speed video cameras towards the place where we had left the prey and waited until the fish was hungry enough to leave the water and catch it," explained Sam Van Wassenbergh, an author on the Nature paper and a biologist from the University of Antwerp, Belgium. "The first time we saw it, we were amazed - it was really spectacular."
The fish captures its prey by propelling itself onto the shore, raising the front part of its body and bending its head downwards over the insect.
Usually, the fish uses suction to feed underwater; but because air is much less dense than water, the fish needs to employ a new strategy to catch its food.
"The way it positions its head prevents the prey from being pushed away," said Mr Van Wassenbergh. "This way it can place its jaws over the prey; and when it is strongly between the jaws, the fish will return to the water where it can further ingest the insect."
C. apus has a specially adapted spine which gives it extra flexibility, allowing it to tilt its head. The fish uses the rest of its long body to maintain stability while it is out of the water.
The best studied fish that feeds on land is the mudskipper. It feeds using a similar method to the catfish, but can use its pectoral fins to hop onto land and to lift and lower its head.
The researchers hope the discovery of another species of land-going fish will help shed light on how sea creatures evolved into land-living tetrapods during the Devonian Period, about 400 million years ago.
They say C. apus bears similarities to fossils found from this period, including the recently described Tiktaalik rosea. This creature, found in Arctic Canada, may be a "missing link" between sea and land-living animals.
"[T. rosea] had a neck that appears to be quite mobile, and strong fins. If you ask me if it could feed terrestrially in a similar way to catfish or mudskippers - I would say it probably could," said Mr Van Wassenbergh.