The blaze was spotted on the mountain slopes behind the academy in Muang district at around 6pm on Thursday.
It broke out just three weeks after soldiers and officials waged a fierce battle to protect the military facility from a large forest fire sparked by lightning.
On Friday, strong winds fanned the flames on Khao Tabaek mountain behind the academy, hampering firefighting efforts of soldiers and officials.
So far, there are no reports of injuries or damage to property.
However, water trucks have been deployed to local communities in a bid to prevent the flames from spreading.
On March 29, a fire that broke out after a lightning strike on neighbouring Khao Laem mountain spread quickly and triggered an emergency response as flames licked at outlying buildings of the military academy.
A large force of soldiers, firefighters and volunteers battled the blaze for five days before it was completely extinguished on April 3.