The evidence comes from beautifully preserved fossil tracks in South Korea.
Nearly a hundred of these 18-24cm-long indentations were left in what were likely the muddy sediments that surrounded a lake in the Early Cretaceous, 110-120 million years ago.
The international team behind the discovery says it will probably challenge our perception of crocodiles.
"People tend to think of crocodiles as animals that don't do very much; that they just laze around all day on the banks of the Nile or next to rivers in Costa Rica. Nobody automatically thinks I wonder what this [creature] would be like if it was bipedal and could run like an ostrich or a T. rex," Martin Lockley, an emeritus professor at the University of Colorado, US, told BBC News.