The group marched from Buchanan High's Veterans Memorial Stadium to the Clovis Veterans Building.
Some of the marchers taking part said they support Ron Paul because of his stance on war.
"We want to give our support to our veterans that are also supporting Ron Paul because we don't want to be sent to wars that are only for the corporations that are making all the money off it. We're for the people and he's here for the rights of the people and our active military veterans," Ron Paul supporter Esteban Rodriguez said.
Sunday's event was intended to mirror a march scheduled for Monday in Washington, D.C. where hundreds of veterans are expected to attend.