Lawyers for the Log Cabin Republicans say they will ask U.S. District Court Judge Virginia A. Phillips on Friday to declare the law unconstitutional.
The case is unique in that it is not based on an individual's complaint but rather is a broad, sweeping attack on the policy. It is the biggest legal test of the law in recent years.
The case has put the Obama administration in the awkward position of defending a policy the president wants repealed. Government attorneys have argued throughout the two-week trial that Congress should decide on the policy — not a federal judge.
They presented only the policy's legislative history in their defense.
The Log Cabin Republicans' witnesses included former officers discharged under the policy and other experts who presented studies of how openly gay troops do not affect unit cohesion or military readiness, as proponents of the law have argued. The group's attorneys also submitted President Barack Obama's remarks that the "don't ask, don't tell" policy weakens national security.
The plaintiff's lead lawyer, Dan Woods, argued the policy violates the rights of gay military members to free speech, due process and open association.
"Don't ask, don't tell" prohibits the military from asking about the sexual orientation of service members but requires discharge of those who acknowledge being gay or are discovered to be engaging in homosexual activity, even in the privacy of their own homes off base.
The group says more than 13,500 service members have been fired under the law since 1994. The 19,000-member Log Cabin Republicans include current and former military members.
Phillips is expected to issue her verdict in writing. Lawyers say she could take weeks or longer to make her decision.
Legal experts say she may hold off to see if Congress is going to repeal it.
The U.S. House voted May 27 to repeal the policy, and the Senate is expected to take up the issue this summer.
In deciding to hear the challenge, Phillips said the "possibility that action by the legislative and executive branches will moot this case is sufficiently remote."
Woods, a Los Angeles attorney from the firm White & Case, said if Phillips rules in their favor and the government appeals, he will ask her to suspend the policy until the case is decided.