The video of the man, identified as Craig McAllister, shows him giving a statement with the barrel of a gun held against his head.
The 12-second clip was uploaded to a file-sharing website on January 10, said SITE Intelligence Group.
McAllister was taken hostage in rebel-held Sanaa in September and said in a video released in October that he had been working in Yemen as a football coach, said the monitor.
In the latest video, he made no mention of what his captors' demands were, but in October's clip he said they were seeking money.
Shiite Huthi rebels overran Sanaa in September 2014, forcing President Abedrabbo Mansour Hadi and his government to flee the capital.
A number of foreigners have been taken hostage in Yemen in the past 15 years, mostly by tribesmen as bargaining chips in negotiations with the government.
Almost all have been freed unharmed.
But in December 2014, US journalist Luke Somers and South African teacher Pierre Korkie died during a failed attempt by US commandos to rescue them from an Al-Qaeda hideout in southeastern Yemen.
