The musician/actor wed ex-pop star Shirlie Holliman in a secret ceremony in St Lucia in 1988, and didn't invite any guests to witness their union.
Now the pair wants to celebrate 25 years together by marrying again in front of friends and family.
Kemp tells Britain's Daily Record, "We will have been married for 25 years this year. We were on our own the first time round and it would be nice to share the day with our friends.
"Our wedding was on a clifftop in St Lucia. It was just me and Shirlie. At the time, I was in the Spandau chaos and Shirlie was part of Wham! and Pepsi & Shirlie.
"The last thing we wanted was a wedding where people were standing next to you taking pictures, so we got away and did it on our own.
"For me, it didn't matter because if you love someone and you want to get married, it really didn't matter where I was. I'd have done it in a registry office and got on with it because I was in love with Shirlie."