Police said the attack took place early on Monday night.
The first grenade landed 20m behind the police station. The explosion caused damage to three cars and the garage. Nobody was hurt.
The second round landed on the southern side of the police station, but did not explode.
An explosive ordnance disposal team examined the scene on Tuesday morning and the destroyed the unexploded grenade.
Police believed the attack was the work of a separatist group led by Aphisi Yuko operating in Lam Mai area of Muang district.
Lam Mai police station has now been the target of four M79 attacks - two this year and one each in 2013 and 2012. The attack on Monday night was the second this year, while the first was on Jan 14. Nobody was hurt in any of the four attacks.