Jack Johnson was convicted by an all-white jury under the Jim Crow-era law and sentenced to a year in prison.
Lawmakers have sent the president a resolution asking for a pardon three times in the last decade, most recently in March.
His great-great niece, Linda Haywood, says in the new video that her family was ashamed Johnson had been railroaded and went to prison. She says he had to sneak around with his white girlfriend and later wife "because of the times that they lived in."
The video was made in Galveston, Johnson's hometown in Texas.