The family's attorney, Robert Mongeluzzi, announced the lawsuit Wednesday.
The lawsuit claims Pub Webb in North Philadelphia over-served Burleigh and Joshua Hupperterz, giving Hupperterz at least 9 shots in just over 2 hours.
The parents of Jenna Burleigh filed the lawsuit against Pub Webb and Hupperterz.
The 31-year-old is serving a sentence of life in prison he was found guilty of murder earlier this year.
Pub Webb's lawyers have asked for the suit to be dismissed.