Fr Tom Uzhunnalil was kidnapped in the Yemeni capital Aden in March this year, after gunmen murdered dozens of nuns and elderly people at a care home nearby.
People who know Fr Tom told the Times of India the man in the video, released on Boxing Day, is definitely the priest.
Fr Tom says in the video that his health is deteriorating and he's suffering from depression.
It's unknown when the video was originally shot. The priest appears to be reading scripted words given to him by his kidnappers.
He says: "Because I was working for the Christian religion, for the church, I was kidnapped.
"Reports have been in the news that everything is being done to get me released quickly, but in reality nothing seems to have happened.
"If I were a European priest I would've been taken more seriously by authorities and people.
"I'm from India and therefore I perhaps am not considered of much value.
"Dear people, I ask you all, beg you all, to do your might [sic] to help me, to save my life. Dear Pope Francis, dear Holy Father, as a father, please take care of my life."
Fr Tom before his kidnapping.
Pope Francis has previously appealed for the release of Fr Tom.
Indian government spokesman Vikas Swarup said: "You are aware of the circumstances currently prevailing in Yemen where fighting is going on with no central authority in that country.
"With regard to the safe release of Father Tom who was abducted some months ago, we have been in regular touch with countries in the region, especially Saudi Arabia as also the local Yemeni authorities. Efforts continue in this regard."
