An efficient (v, r, n)-fairness secret sharing scheme is proposed in this paper. In the proposed scheme, all participants have an equal probability to recover the shared secret, even if there exist v cheaters, v<r/2, among the n participants. To put it another way, if the cheater can recover the shared secret in the recovery phase, the honest participants can recover the shared secret too, and vice versa. Furthermore, we show that our (v, r, n)-fairness secret sharing scheme is more efficient than Lee and Laih's scheme.