For controlling the public verifiability of ordinary digital signatures, designated confirmer signature (DCS) schemes were introduced by Chaum in 1994. In such schemes, a signature can be verified only with the help of a semi-trusted third party, called the designated confirmer. In this paper, we propose a new DCS model - designated confirmer signature with specific verifier (DCSSV), in which both the signature verifier and confirmer were appointed by signer, and instantiate it with an efficient construction. The new scheme is transformed from ID-based chameleon signature and inherits its advantages in simplicity and efficiency. The scheme?s security relies on the underlying secure chameleon signature and public key encryption scheme. In addition, the case of confirmer as an adversary was also considered in our security analysis.