The 29-year-old started 15 games for the Browns during his debut season, missing the final fixture because of injury.
Weeden told the Cleveland Plain Dealer: "I completely expect to be the starter. That's my mindset going in.
"I'm confident in my ability to be the guy, to lead this football team. I expect completely to be better this year than I was last year."
Weeden has previously said that he expects to face competition for the role.