In this paper we propose a new designated verifier signature scheme based on the threshold signature scheme presented [8] by Ghodosi and Pieprzyk. The advantages of the new scheme compared with previously proposed solutions are its computational efficiency and its simple and rational design that allows distributed implementations of the computations and suits the needs of both single individuals and organizations wishing to set a threshold on the number of required signers. The signing key size remains bounded by the size of a RSA modulus. Moreover, in addition to the computation of a classical RSA signature, the signature generation of our scheme needs only one modular multiplication; the verification process in our scheme remains the same than a classical RSA signature verification.