The 28-year-old striker has linked up with the Tigers on a season-long loan after falling out of favour at Sunderland.
Graham made a £5million move to the Stadium of Light in January, but failed to find the target in 11 outings for the Black Cats.
He is now looking to reignite his career at the KC Stadium and admits he would be open to extending his stay with Hull if he can deliver the goods and help Steve Bruce's side to preserve their Premier League status.
Ahead of a trip to Chelsea on Sunday, Graham told The Sun: "I am confident I can start scoring goals in this league again.
"I've had these sort of spells before in my career - you have your highs and your lows.
"It's easy to walk around with your head held high when everything is going your way, but if it's not going my way I always keep my head up. And it happens to the best of players, so why should I let it drag me down?
"For the gaffer to take a punt on me when I hadn't scored for so long shows a lot of faith.
"I'm going to pay him back by scoring goals and making sure Hull stay in the Premier League."
On his future, Graham added: "I'm here for a season but if I'm playing and doing well I'd be looking to make it permanent."