Pupils at 10 primary schools and one secondary school will have the chance to earn the vouchers, worth between 50p and pound;15. The trial will be funded by Leicester city council.
Each school will receive special packs containing pound;500 in vouchers, and these will be awarded for achievements, ranging from good behaviour to attendance, punctuality and outstanding homework or sporting achievement.
The pupils will be able to exchange the vouchers for entrance fees to leisure centres and summer play schemes in the city.
If the term-long trial is successful, the city plans to extend it to all 64 primary school and 20 secondary schools. The primary schools chosen are all feeder schools to Lancaster School - a secondary which has already been awarded the government's specialist status for sport.
Lancaster headteacher, Ed-mund Blount, has warmly
welcomed the scheme, saying: "I think it's a wonderful idea for the children and will give them something to aim for."
David Dunmore, headteacher at one of the feeder primaries, St John's Church of England school, called it an "excellent initiative". His school plans to use the money-off vouchers to reward sporting achievements.
"It seems an innovative way of encouraging children to exercise properly and concentrate on physical fitness by giving them a tangible reward," he said.