The submarine with three people on board, including Tsunemi Kubodera from the museum, followed the enormous mollusc to a depth of 900 metres as it swam into the ocean abyss.
NHK showed footage of the silver-coloured creature, which had huge black eyes, as it swam against the current, holding a bait squid in its arms against the backdrop of dark oceanic depths.
The creature was about three metres long, but "estimated to be as long as eight metres if its two long arms had not been chopped off", Kubodera told AFP.
He gave no explanation for its missing arms.
He said it was the first video footage of a live giant squid in its natural habitat -- the depths of the sea where there is little oxygen.
Kobudera, a squid specialist, also filmed what he says was the first live video footage of a giant squid in 2006 but only from his boat after it was hooked and brought up to the surface.
The giant squid, "Architeuthis" to scientists, is sometimes described as one of the last mysteries of the ocean, being part of a world so hostile to humans that it has been little explored.