The 37-year-old helped Town to promotion from League One this season, with eye-catching displays against Crewe and Barnet at the end of the season.
Kuipers will also aid the development of the young goalkeepers at the club.
He told Crawley's official website: "I'm really looking forward to next season, it's going to be challenging but we've got a good squad already and we'll be adding over the summer.
"I'm looking forward to developing the younger goalkeepers and working with the first team too. We will try to develop a goalkeepers' union and if we can run that through all the youth team hopefully it will produce some very good keepers."