The 25-year-old Ghana international scored 11 goals, 10 of them in the league, during his first campaign on Wearside, but is confident he will make an even bigger contribution this time around.
Gyan told the Sunderland Echo: "I'll definitely be a better player next season.
"As I said before I came here, it was my dream to play in the English Premier League. I feel I have established myself now, but there is more to come.
"The fans love me which is really important. When the people are behind you, you keep going and I hope to do more.
"It depends on me keeping working hard. There are some seasons where things don't go well, but that doesn't mean you are a bad player."
Gyan arrived at the Stadium of Light in a £13million-plus switch from French club Rennes in August last year, and having played a major role in his country's World Cup finals adventure in South Africa, was eased into Steve Bruce's team.
However, he believes a full pre-season and the experience he now has under his belt can only improve him this time around.
He said: "It's the most difficult league in the world and you need to be 100 per cent fit to survive, which I wasn't when I arrived.
"There have been plenty of good players who have come to the Premier League and not done well, so it just shows how difficult it is."
Gyan will be the senior man in a new-look strike-force with 18-year-old Connor Wickham and South Korea international Ji Dong-won having been drafted in last week.
He himself has been linked with a move away from the club this summer with Tottenham touted as a possible destination.
Indeed, his agent Fabien Piveteau has suggested the player will hold talks with Bruce on his return and that at least one offer has been received, something sources on Wearside have dismissed.
Gyan and his team-mates are due back for the start of pre-season training on Wednesday, and they could soon be followed by further new faces with Bruce and chairman Niall Quinn continuing their efforts to land Manchester United trio John O'Shea, Wes Brown and Darron Gibson.
It is understood significant progress has been made with O'Shea and Brown in particular, but that nothing is yet complete despite the Black Cats having a joint bid of more than £12million accepted some time ago.