Though construction on Square 54 has stayed on schedule this summer and is slated for completion in 2011, no new leases have been signed for the property, the site’s developer said.

The mixed-use project, located across the street from GW Hospital, will be complete in the first quarter of 2011, and construction is currently centered on the first floor, Boston Properties Senior Project Manager Jake Stroman said in an e-mail.

“We are currently framing and will be pouring the first-floor slab of the office building, courtyard, and residential building in the coming weeks,” Stroman said.

Despite the ongoing construction, only one signed lease has been announced so far. Hunton & Williams, a law firm, signed a lease for 190,000 square feet of the development last fall. Square 54 has a total of 450,000 square feet of commercial office space, over 300 rental apartment units, and 84,000 square feet of retail space on the 2.6 acre site at 2200 Pennsylvania Ave.

Stroman said Boston Properties is still in negotiations with a tenant for space allotted for a full service grocery store, but said he cannot disclose which supermarket chain it is. The Washington Business Journal reported in February that Giant Food was in negotiations with the company.

Summer construction work has included concrete work on the building’s below grade garage structure, and utility work has closed an additional lane of traffic on 22nd Street between I Street and Pennsylvania Avenue since the first week of August, according to construction updates. The lane has been closed Monday through Saturday from 9:30 a.m. to 3 p.m.