Kelly's comments were in an opinion piece in the Houston Chronicle as about 70,000 people made their way to the city for the NRA's annual convention, which began Friday and runs through Sunday.
Kelly, a retired astronaut and U.S. Navy captain, said the NRA leaders, including Wayne LaPierre, the organization's chief executive, turned their backs on the group's traditional values to attain profit.
He called on them to step down.
"LaPierre and the gun manufacturers he represents exploit people's fears," Kelly wrote. "In return, gun manufacturers gave LaPierre and the NRA tens of millions of dollars last year alone -- and he spent almost $1 million of it on his own salary."
The convention comes just weeks after gun-control legislation failed in the U.S. Senate despite the public's support of an expansion in background checks.
Among people at the convention Friday was Drew Kelley, who works for a firearms manufacturer based in Los Angeles.
"The whole idea [of background checks] was to keep people who should not have guns from acquiring them," Kelley said. "But the people who they're talking about don't go through the normal commercial processes anyway."
Giffords was shot in the head Jan. 8, 2011, in an attack in Tucson that killed six people and wounded 18 others besides the congresswoman.