Speaking on "Fox News Sunday," Thompson -- an actor, lobbyist and former Tennessee senator -- said he wants to maintain the 2001 and 2003 tax cuts, eliminate the estate tax and reduce the corporate tax rate.
"We have the second-highest corporate tax rate among our competing partners," Thompson said. "It's hurting us competitively. We're probably losing revenue from it."
Thompson said he would like to see passage of a House Republican proposal that would allow taxpayers the option of continuing to file as they do now or try a new system that would only have two rates with no exemptions, other than the personal exemption, and no deductions.
"So give that a try and it would be a major move toward tax reform, which I think is greatly needed," he said.
He rejected contentions his plan would result in a 10 percent drop in total tax revenues.
Thompson also said he wants to see a move toward personal savings accounts and indexing initial Social Security benefits to inflation rather than wages.