Stephon Tull told CNN he discovered the tape marked "Dr. King interview, Dec. 21, 1960, while rummaging through boxes in his father's attic.
Tull said he borrowed an old tape player so he could listen to his father interviewing King.
"I could not believe what I was hearing," said Tull, whose father had grown up in Tennessee during the years of racial tension and segregation laws.
"He planned on writing a book on how bad things were back in that era," Tull said, but never finished it.
In the interview, King discusses his definition of non-violence and its importance in the civil rights movement.
In another part, the civil rights leader talks about a recent trip to Africa.
Historian Clayborne Carson, founding director of the Martin Luther King Jr. Research and Education Institute at Stanford University, said he and his colleagues are most interested in what King says about Africa on the tape.