They also called on the General Assembly to eliminate a current statute governing the election of BOG members.
The lawsuit, served May 30, claims that it is unconstitutional to set aside seats at the Board of Governors for specified groups of people.
The quota system has allegedly prevented some of the plaintiffs from becoming members of the BOG.
As of now, there are two statutes regulating diversity in the BOG: The first states generally that different races, sexes and political parties should be represented; the second stipulates that four seats on the 32-member BOG should be reserved for a racial minority, four for members of the largest minority party in the General Assembly and four for women.
The lawsuit challenges the second statute, but not the first.
"I would say it is almost impossible (for the BOG) to win this lawsuit under existing case law," said Eugene Boyce, one of the three attorneys who filed the suit.
The board also thought it would be difficult to fight the lawsuit, BOG Chairman Benjamin Ruffin said in a statement released Friday.
The BOG requested that its attorneys ask the General Assembly to amend the statute under consideration and drop entirely the portion that specifies quotas, according to the statement.
The lawsuit was filed by five plaintiffs, including Walter Davis, a long-time contributor to the Democratic Party and Barbara Howe, former Libertarian candidate for governor.