The video, sent to the Nigerian government, shows 15 girls in black robes identifying themselves as pupils abducted from the secondary school.
Some of those filmed have been identified by their parents.
It is the first footage of the girls to be seen since May 2014.
The kidnapping of the 276 girls triggered the global social media campaign #BringBackOurGirls, involving US first lady Michelle Obama and a host of celebrities.
But despite their efforts, most of the girls are still missing.
Meanwhile, hundreds of parents are due to hold a march in the Nigerian capital, Abuja, to demand the government does more to find their daughters.
The BBC’s Martin Patience in Abuja says they blame the previous government for doing nothing when the abduction took place and now the current administration for failing to devote enough resources to the search.
Boko Haram militants attacked the government boarding school in Borno state on 14 April 2014, seizing the girls who had gone there to take exams.
Shortly afterwards they released a video of them and demanded a prisoner exchange.
Boko Haram’s leader, Abubakar Shekau, said the girls had converted to Islam and he threatened to force them into marriage with his fighters or sell them into slavery.
As the months passed, about 57 students managed to escape but at least 219 are still missing.
The latest video, apparently filmed on Christmas Day 2015, shows the girls pleading with the Nigerian government to co-operate with militants on their release.
They said they were being treated well but wanted to be with their families.
Two mothers, Rifkatu Ayuba and Mary Ishaya, said they recognised their daughters in the video while a third mother, Yana Galang, identified five of the missing girls, Reuters reported.
They were shown the video at a screening organised by local officials in Maiduguri, capital of Borno state.
“They were definitely our daughters… all we want is for the government to bring back our girls,” said Mrs Galang.
Amnesty International says about 2,000 children have been abducted by Boko Haram since 2014. Many are used as sex slaves, fighters and even suicide bombers.
Although the militants are still launching attacks, the Nigerian army has made progress in its fight against them over the past year, our correspondent adds.
It has retaken towns and villages controlled by Boko Haram and has also freed hundreds of women and children held captive.