A $40 million office complex in Southwest Washington will be used to try out a new District of Columbia plan to cut the red tape that often delays major construction projects, Mayor Marion Berry Jr. announced yesterday.

The mayor said the District will appoint a government "project manager" to expedite issuing the dozens of licenses, permits and certificates needed to build a big development.

Designation of a single city official to oversee the project is the first step toward creating a "one-stop" permit process for construction approvals, city officials said. If the concept succeeds, it will be adopted for other large developments.

During the mayoral campaign, Barry promised to act on developers' complaints that it frequently takes as long as a year to complete all the municipal paperwork needed to start construction.

The pilot project for cutting the red tape will be Capital Gallery, a block-square complex at 600 Maryland Ave. SW, near L'Enfant Plaza.

Capital Gallery is the final building in the Southwest urban renewal area, where redevelopment has been under way for almost 20 years.

Developers of the project are Boston Properties Inc., and Travenca Development Corp., a minority-owned Washington firm headed by T. Conrad Monts.

Boston Properties, which holds controlling interest in the project is a Massachusetts-based builder that operates more than 4.5 million square feet of offices in Boston, Los Angeles, San Francisco and Philadelphia.

More than a million square feet of additional development is now being built by Boston Properties, including the Power House Hotel in downtown Baltimore.

Capital Gallery will be a $630,000 square foot office complex comprised of an eight-story office tower and a three-floor building linked by a three-story, glass-walled gallery of retail shops.

The George Hyman Construction Co. is beginning work now on the complex to be completed by the spring of 1981.