The parents say Stewart had complete disregard for Kevin's life a year ago when his race car struck and killed the 20-year-old.
The lawsuit claims Stewart gunned his 700 HP car as he drove by Ward. Stewart's car slid and struck Ward with the rear tire, hurling him 25 feet. The suit claims Stewart gunned the engine to "terrorize" Ward.
There were rumors of beef between the two, which fueled speculation Stewart intentionally plowed into Ward with his car when he ran onto the track ... something he denies.
Stewart was cleared of criminal charges. Authorities also say Ward was high on weed when he got out of his car.
Ward's family still believes the death was avoidable and they want to take it to a civil jury.
Reps for Stewart have no comment.