The cheat-proof method in threshold secret sharing scheme is researched. The threshold secret sharing scheme is integrated with RSA and one-way function. And the RSA and one-way function are fully utilized to verify the validity of data. A threshold secret sharing scheme based on RSA is proposed, at which the cheating is equal to attacking RSA scheme. A threshold secret sharing scheme based on RSA and one-way function is also presented, at which the cheating is equal to attacking RSA scheme or one-way function. These two schemes have so strong power to identify cheaters that they can restrict the probability of successful cheating to a very small value no matter how skilled cheaters are, so they are unconditionally secure. In addition, the schemes proposed in this paper have very high information rate.