Comet the goldfish can also play fetch with a hoop, slalom around a series of poles and push a rugby ball over a set of posts.
Dr Dean Pomerleau, 41, from Los Angeles, used a training technique called positive reinforcement to train two-year-old common goldfish Comet to carry out the tricks.
He said: "There is mounting evidence that fish are more intelligent than people give them credit for.
"With the correct tools and the basic promise of a food reward, fish can very quickly learn complex tricks - like the limbo, slalom or playing fetch.
"Now people in the market for a dog might want to consider a fish instead."
Positive reinforcement is a training technique where the fish is rewarded with food when he successfully completes a task.
Dr Pomerleau added: "We've used techniques that we've customised for pet fish, but are based on those used to train dolphins and other marine mammals."
He has teamed up with pet product firm R2 Solutions to design a special kit to help people train their fish. It features goal posts, slalom poles and tunnels, as well as an instructional DVD.
The R2 Fish School kit is available from online retailer Amazon for around £16.