"I think the assault weapons ban didn't work then. It's not going to work now, and I will oppose it," Graham said on "Fox News Sunday."
Sen. Dianne Feinstein (D-Calif.) plans to introduce a new federal assault weapons ban in the next Congress. And on Sunday, President Obama said he wanted to sign into law new gun-control measures in 2013.
Graham said the last assault weapons ban, which lasted for ten years, was ineffective.
"Well, we had the assault weapons ban from 1994 to 2004 and the conclusion was, it did not change crime by banning assault weapons in an appreciable way, and last year with the lowest murder rate in the history of the United States, people buying more guns, murder rates have gone down -- you are talking about preventing mass murder by mentally unstable persons," Graham said. "You can't take every sharp object out of the reach of people like this."
Graham suggested he supported a proposal by the National Rifle Association (NRA) to post armed guards in schools to prevent shooting massacres similar to Sandy Hook.
"I own an AR-15 and I have done nothing wrong by owning the gun. If you had armed security, with better rules of engagement, that, to me, is a better way to deal with the situation," Graham said. "And the best way is to identify these people before they act and do something about it."