Edward Beavis, 34, of no fixed address, pleaded guilty to arson and criminal damage, at Salisbury magistrates court.
If follows a fire at Avenue Primary School in Warminster, in which two classrooms were destroyed. Nobody was injured in the blaze.
He is due to be sentenced at Salisbury Crown Court on date yet to be decided.
A man has admitted setting fire to a primary school which was partially destroyed in a blaze early on Wednesday.