The 32-year-old, who has been with Albion since 2000 but made just 18 starts last season, is keen to re-establish himself as first choice.
"I spoke with the manager at the end of last season, I'm fully behind his thoughts," the Dutchman told BBC Southern Counties Radio.
"I want to start every game - every player should have that mentality."
Kuipers' deal includes an option for a further year.
Midfielder Doug Loft has also penned a new one-year contract at Withdean.
