The British actor was best known for playing Admiral Motti in 1977's Star Wars Episode IV: A New Hope.
In one of the film's most iconic scenes, Motti was Force-choked by Darth Vader for insubordination.
The circumstances of the actor's death have yet to be confirmed, TMZ reports.
LeParmentier starred in over 30 films and TV shows during his career, including roles in Who Framed Roger Rabbit? and Stardust.
He was married to British actress Sarah Douglas from 1981 to 1984, and both appeared in Rollerball, The People That Time Forgot and Superman II.
He also had roles in Octopussy and the TV shows Capital City and We'll Meet Again.
LeParmentier once said of his most famous role: "I did the choking effect by flexing muscles in my neck. It set off a chain of events, that choking.
"I can't do it anymore because, oddly enough,