A £415,000 carbon-fibre winged prototype, called the Necker Nymph, is already being developed that can submerge to depths of 130ft (40m).
Sir Richard told The Sun: "It is very similar to an airplane flying in the sea. You can literally do a loop-the-loop."
But it is only the first step to his greater ambition to take one to the dark depths of the Mariana Trench in the Pacific, which is 36,000ft (11,000m) deep.
The Nymph will be moored on Sir Richard's private Caribbean island, Necker.
He said: "We hope to have submarines dotted throughout the world.
"A pressurised submarine is nearly completed. But the real challenge is to explore what's going on at the bottom of the oceans."
The Nymph is being built by Hawkes, an American company. It has three bubble cockpits giving occupants wide-angle views and is steered with a joystick, like some fighter jets.
James Cameron, who directed The Abyss, used one of them while researching his 3-D film Avatar, according to the paper.
btw Richard Branson is the shit
tats awesom this dudes got talent