Based on Chameleon Hash and D. Boneh's one round multi-party key agreement protocol, this paper proposes a multi-designated verifiers signature scheme. In this scheme only the verifiers designated by the signer can independently verify the signature. And no one else other than the designated person can be convinced by this signature even if one of the designated verifiers reveals the secret value. The analysis of the proposed scheme shows that it satisfies non-transferability, unforgeability and privacy of the signer's identity and has to low computational cost.