The star of "Armageddon" and "The Green Mile" is buried in Forest Lawn Cemetery. He died last year, following complications from a heart attack. He was 54.
TMZ said a friend was delivering flowers to his tomb when she spotted an image she said is "Sambo," a figure long considered an offensive and racist depiction of a black person.
Duncan's family, upset by the incident, contacted the Los Angeles Police Department. The image was removed from the actor's grave, TMZ said.