"Three or four thousand American troops with some air capability we don't have today will turn the tide of battle," Graham told reporters.
President Donald Trump and his top advisers are currently immersed in an effort to craft a new strategy for Afghanistan.
Graham said Trump would do well to heed the advice of his generals, including National Security Advisor H.R. McMaster.
"If we do not listen to General McMaster and people like him, who have been fighting this war for 15 years, and adapt our policies, we're going to fail in Afghanistan," Graham said.
The senator also said if the United States does not add the extra capability to the fight, the situation will get worse to the extent that the developments seen in Iraq will happen tenfold in Afghanistan.