Based on Shamir s secret sharing, a (t, n)multi-secret sharing scheme is proposed in this paper. p secrets can be shared among n participants, and t or more participants can co-operate to reconstruct these secrets at the same time, but t-1 or fewer participants can derive nothing about these secrets. Each participants secret shadow is as short as each secret. Compared with the existing schemes,the proposed scheme is characterized by the lower complexity of the secret reconstruction and less public information. The security of this scheme is the same as that of Shamir s threshold scheme. Analyses show that this scheme is an efficient, computationally secure scheme.