He started Tuesday at an Anchorage shooting range and shot a variety of hand guns and rifles.
Kelly hoped to emphasize that he and Giffords support Second Amendment rights but believe additional background checks will save lives and keep guns out of the hands of those who shouldn't have them.
Giffords survived a 2011 attack in Arizona.
The couple is on a seven-state, "Rights and Responsibilities Tour." They hope to persuade Alaska's two U.S. senators to change their votes against expanded background checks.
Tuesday's stop also includes a round-table discussion with gun owners.