In the three-minute video, the AQAP gave the US government three days to meet a series of demands which it said the White House had already been informed, or they would kill Luke Somers, 33, an American journalist who was kidnapped in September 2013 in the capital Sanaa, Xinhua reported.
The AQAP also warned the US not to conduct "any further stupid mission on the Yemeni soil" to seek to rescue Somers.
Somers, who appeared in the video, pleaded for help to secure his life.
"It has now been well over a year since I have been kidnapped in Sanaa. Basically I'm looking for any help that can get me out of this situation," Somers said.
"I'm certain that my life is in danger."
Last week, US and Yemeni special forces conducted a rescue operation in the southeastern province of Hadramout, setting free six Yemeni hostages.
Somers was among five hostages, including a Briton and a South African, believed to have been moved away before the rescue operation.