The U.S. Food and Drug Administration awards certain drugs priority status when they have the potential to offer significant improvement over existing treatments.
The agency is due to give its verdict on whether to approve dolutegravir by Aug. 17, the drugmaker said on Friday.
The once-daily drug, which belongs to a novel class known as integrase inhibitors that block the virus causing AIDS from entering cells, is owned by ViiV Healthcare, a joint venture focused on HIV in which GSK is the largest shareholder.
The new medicine has already performed strongly in clinical trials, prompting GSK to raise its bet on the product last October by redrawing a deal with Japan's Shionogi.
Under that agreement Shionogi agreed to take a 10 percent stake in Viiv - which was set up in 2009 between GSK and Pfizer - in exchange for its shared rights to dolutegravir.
The agreement left GSK holding 76.5 percent of ViiV, with Pfizer controlling 13.5 percent and Shionogi the remainder.
Analysts see dolutegravir as a strong competitor to HIV treatments from market leader Gilead Sciences.