The university is infringing on students' First Amendment right to religious freedom by requiring them to read "Approaching the Qur'n: The Early Revelations," says the suit, filed Monday in federal court in Greensboro.
All incoming freshmen this year have been told to read the text, which includes 35 translated sections of the Quran, the holy book of Islam. They also are expected to attend discussion sessions Aug. 19.
School officials have said the subject is timely and informational, and that the reading requirement is not intended to promote Islam.
Last week, UNC amended its policy to say students who are offended by the book don't have to read it, but they are required to write a one-page paper stating their objections.
The lawsuit was filed by the Virginia-based Family Policy Network and three UNC freshmen identified only as John Doe No. 1, an evangelical Christian, John Doe No. 2, a Catholic, and Jane Roe, who is Jewish.
"Our long-term goal is to make sure the precedent is affirmed that you cannot force people to take a class about a religious text at a state university," said Joe Glover, president of the Family Policy Network, a nonprofit conservative group.
A university spokesman said school officials would not comment on pending litigation.