In this paper, we propose a secure rewarding scheme. In the scheme, a reward provider publishes a problem, and provides a reward for a person who can supply him a satisfactory solution of the problem. The first qualified claimant with satisfactory solution of the problem is selected to obtain the reward. The selected claimant can obtain the reward from the reward provider with- out revealing his identity. Nobody except the selected claimant can get the reward, and the provider cannot decline the selected claimant his entitled reward. In addition, we also propose another secure rewarding scheme with two-way untraceability to protect the privacy of the reward provider as well.