The army will pay $11,000 for information on the whereabouts of the leader of the 15-year old rebellion.
It has also put a price on the heads of the top commanders of the rebel group, an estimated 38 of them, which is feared for its brutality and cruelty.
Joseph Kony and his commanders are believed to be hiding in southern Sudan and northern Uganda.
But the army statement says a three-year-old amnesty offer is still open to the rebel leaders.
Tethered
Last week, Sudan agreed to let Ugandan soldiers remain on its territory in order to pursue the LRA.
They had earlier said the agreement, first made in March, would not be renewed.
Army spokesman Major Shaban Bantariza told the BBC's Focus on Africa programme that the LRA leader was "mobile, not tethered like a goat", making it difficult to find him.
"They are trying to hide as small groups and individuals, they are likely, even, to try to hide in people's houses, so we are giving this money as an incentive to the population so they can give us any information to the leaders, smoking them out of those hidings," he said.
"There's no army in the world that wins a war alone. Even the USA has put a reward on the head of Bin Laden."
Biblical rule
Among the 25 other suspected LRA leaders with prices on their heads are James Opoka, political assistant to opposition leader Kizza Besigye and the LRA deputy leader, Vincent Otti.
The LRA has been fighting the government of President Yoweri Museveni for 15 years, demanding that Uganda be ruled according to the Biblical Ten Commandments.
But it has kidnapped thousands of children for use as fighters or sex slaves.
Despite being allowed to use Sudanese territory since March, the Ugandan army has been unable to stop LRA attacks.
The rebels have fled their bases in Sudan and entered northern Uganda, where they have intensified their attacks.