The Log Cabin Republicans has about 19,000 members who support gay rights. In court, the group will argue that people have a constitutional right to live a homosexual lifestyle, and "don't ask, don't tell" violates that right.
The law prohibits the military from asking about the sexual orientation of service members, and it requires discharge of those who acknowledge being gay or are discovered engaging in homosexual activity.
President Barack Obama has criticized the policy and is working with Congress to repeal it through federal legislation, but critics say the president hasn't acted fast enough since taking office.
The U.S. House has voted to repeal the policy, and the Senate is expected to take up the issue this summer.
If the Log Cabin Republicans win their case, they'll ask U.S. District Judge Virginia Phillips to halt "don't ask, don't tell" immediately.
The trial begins Tuesday and is expected to last about two weeks.