Abubakur Shekau's presence in the video directly contradicts the Nigerian government's claims that he's been killed and that Boko Haram is close to being crushed.
Nigerian President Muhammadu Buhari declared last week soldiers had driven Boko Haram from its last forest enclave in the north-east, boasting "the terrorists are on the run, and no longer have a place to hide".
In a video posted on YouTube, Abubakar Shekau said: "I am here, well and alive" and that "the battle is just beginning".
Boko Haram is responsible for the murder of 20,000 people, many of them Christians, as well as driving 2.6 million from their homes.
Christian Aid reported earlier this week that 1.8 million people were in urgent need of food, water and sanitation supplies because of Boko Haram.
The Islamist militant group also kidnapped 276 schoolgirls, most of them Christian, from the town of Chibok in 2014. The vast majority are still being held hostage by them.
Nigeria's military has claimed to have killed Abubakur Shekau at least three times and earlier this year declared he had been fatally wounded.
This week, the army said it had seized Shekau's Koran in the Sambisa Forest during an assault.
Each time such claims of his death are made the Boko Haram leader reappears in a video to mock them.
In the latest, posted on YouTube on December 29, he says: "Kill all the infidels and detonate bombs everywhere.
He makes no mention of the missing Chibok schoolgirls.
