In the setting of secret sharing, one desirable property is fairness, which guarantees that if there is a player getting the secret in the recovery phase, then each player participating to the reconstruction process does too. In this paper we study the fairness problem of secret reconstruction in a secret sharing scheme. We use a new approach to achieve the fairness of secret sharing. We first define the fairness of secret sharing probabilistically. Based on this definition, a fair secret sharing scheme is proposed, its security and fairness are shown against three different attack types and do not depend upon any unproven intractability assumption. Our scheme is an extension of Shamir's secret sharing scheme and the approach of fairness of Dov Gordon et al.(STOC2008). Theoretical analysis shows that our proposed scheme is more efficient.