The NLRB complaint says Boeing engaged in unfair labor practices against the International Association of Machinists and Aerospace Workers union by moving the 787 work to discourage union strikes, a protected activity.
The NLRB scheduled a June hearing on the matter.
Boeing, the world's second-largest commercial plane maker, said it would vigorously contest the complaint.
Boeing has every right under both federal law and its collective bargaining agreement to build additional U.S. production capacity outside of the Puget Sound region, said Boeing General Counsel J. Michael Luttig in a statement.
The complaint says Boeing made coercive statements to its employees that it would remove or had removed work from the unit because employees had struck, the NLRB complaint states.
In 2008, Boeing endured a 58-day strike over a contract dispute.
The federal labor board is seeking an order requiring Boeing to operate the second 787 line in Washington state, where union workers build the company's commercial planes. Boeing Commercial Airplanes is based in Washington, where its primary assembly plants are in Everett and Renton.
Boeing opened a second, nonunion production line for its 787 Dreamliner in South Carolina after an aggressive campaign by workers in Washington's Puget Sound area to keep the project there.
By opening the line in Charleston, Boeing tried to intimidate our members with the idea that the company would take away their work unless they made concessions at the bargaining table, said Tom Wroblewski, president of Machinists Union District Lodge 751 in Seattle.
The Dreamliner is about three years behind its original schedule because of problems with the extensive global supply chain. Boeing also blames the 2008 strike for one of the delays.
(Reporting by Kyle Peterson and Karen Jacobs; Editing by Steve Orlofsky)