The Wales international reclaimed the gloves from the recently departed Marcus Hahnemann last November, going on to notch up 24 Premier League appearances for the Midlanders.
The exit of Hahnemann has prompted Wolves to sign Dutch keeper Dorus De Vries this summer, while reserve shot-stopper Carl Ikeme is fully fit following a string of injuries.
Manager Mick McCarthy has already indicated he wants the trio to compete for the first-choice spot ahead of the new season.
But 24-year-old Hennessy has no intention of relinquishing the number one role, telling Wolves' official website: "I felt really good last season.
"When I did get into the team I thought I did well and hopefully I can continue like that.
"I managed to play 24 league games which was good and my aim now is to try and play for a whole season.
"We all set ourselves targets as players and try and reach them and it's all about trying to improve all the time.
"I still think I have more to come and it's just good to be back and looking forward to another season."
Wolves are set for their third successive campaign in the top-flight and Hennessy hopes they can improve on last season.
"We got more points last season than the one before and I think that gives us something to aim for again," he said.
"To try and get more points than we did last season.
"There are never any easy games in this league but it's a great league to be part of.
"It is going to be difficult but it's a challenge we are all looking forward to."