The law, passed by the Legislature at the end of its recent session, splits the Omaha district starting in 2008 into three districts: one mostly black, one largely Hispanic and one predominantly white.
It was aimed at solving a dispute over school boundaries in the state's largest city after Omaha Public Schools tried to take over some suburban schools.
The NAACP's federal lawsuit says the new law violates the constitutional principals embodied in the 1954 U.S. Supreme Court ruling in Brown vs. Board of Education, which said separate but equal facilities have no place in public education.
"Segregation is morally wrong, regardless of who advocates it," said Tommie Wilson of the Omaha chapter of the NAACP.
Supporters said the plan would give minorities control over their own school board and ensure that their children were not shortchanged.
State Sen. Ernie Chambers, the Legislature's only black senator, has long argued that the Omaha district was already segregated because it no longer bused students for integration purposes.
The NAACP and Omaha Public Schools officials opposed the new law, saying it was short on funding and would do too little to promote integration — even hampering other efforts.
The NAACP wants the Legislature and Gov. Dave Heineman to come up with a workable alternative to the new law by January, said John Jackson, the national NAACP's chief policy director.
Heineman, who signed the legislation, has said provisions of the law were subject to changes.
The 45,000-student Omaha school system is 46 percent white, 31 percent black, 20 percent Hispanic, and 3 percent Asian or American Indian.