In a strong designated verifier signature scheme, a signer can issue a signature for a special receiver; i.e. only the designated verifier can verify the validity of the issued signature. Of course, the signature scheme should be such that no third party will be able to validate the signature. In other words, the designated verifier cannot transfer the issued signature to a third party. In this article, we propose a new ID-based designated verifier signature scheme that has provable security in the random oracle model and BDH assumption. The proposed scheme satisfies all security requirements of an IDVSS. In addition, the proposed scheme protects from user's privacy and from the efficiency point of view, and more precisely, in terms of parameters such as the size of output signature and computations required for signing and verification phases. As a result, our proposed scheme is comparable with other existing schemes; in other words, the proposed scheme is a light-weight construction. Finally, we introduce some practical scenarios of the proposed scheme in the Internet of Things concept.