"Here I am, alive. I will only die the day Allah takes my breath," Shekau said in a 36-miute video, adding that his group was "running our...Islamic caliphate" and administering strict sharia punishments.
In the video, Shekau is seen speaking in Arabic and the Hausa language widely spoken in northern Nigeria.
However, there is no indication of where and when was the video shot.
Earlier, the Nigerian military has made such claims about Shekau's death in 2009 and in 2013.
This year too, the claims of Nigerian military over Shekau's death turned out to be hoax.
Last week, on Sept 25, Thursday, Nigerian security forces claimed to have killed the leader of Boko Haram militants, Abubakar Shekau.