No group has claimed responsibility for the abduction in the city of Bamenda, which lies in the English-speaking region of the African country.
Separatists are fighting to form a breakaway state in the region and they have called for a boycott of schools.
According to the Journal du Cameroun, gunmen stormed the Presbyterian Secondary School in the Nkwen district of the city and rounded up pupils.
The Principal of the school, a driver and another teacher were also kidnapped, the paper reported.
The separatists have imposed curfews and closed down schools as part of their protest against President Paul Biya's French-speaking government.
"In total 81 people were kidnapped including the principal. They were taken to the bush," a military source told Reuters.
A government spokesman said it was keeping track of the situation but could not comment further.
The Presbyterian Secondary School is described as a co-educational Christian public boarding school founded in 2001.
It has more than 700 students and “prides itself with students from all religious and linguistic backgrounds in Cameroon”.
Hundreds have been killed in Cameroon’s Anglophone regions in the past year in violence between armed separatists and the military.
Violent separatists took up arms to destabilize the Anglophone regions to win independence for the areas they want to declare a separate state, which they call Ambazonia.
Many people have fled Bamenda and other centres to seek refuge in more peaceful Francophone regions.
Cameroon has also come under attack from Boko Haram after the Islamist militants most of their territory in neighbouring Nigeria.
They shocked the world when they kidnapped 276 schoolgirls from the town of Chibok in Nigeria
That prompted a high profile social media campaign that saw everyone from Michelle Obama to David Cameron demand they "bring back our girls."
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