The soldier prince made the revelation in a television interview to promote his support for the Teenage Cancer Trust's plans to build a new centre for young patients at the Royal Marsden Hospital in Sutton, Surrey.
The 26-year-old, who is presently training to become a Royal Air Force search and rescue pilot, unwrapped his childhood ambition in front of a 10-year-old cancer patient Alice who asked him what he would have done if he were not a prince.
"A long time ago I wanted to be a policeman. I soon learned that probably wasn't a good idea," the Sun quoted him as saying in an interview with the BBC's Newsround.
And when asked who would win an arm wrestle between him and his younger brother Prince Harry, he added: "You know the answer to that! It's not even a contest.
Obviously I'd win. As the bigger brother you have that psychological power over your brother, you see."