In an identity-based designated verifier proxy signature (ID-DVPS) scheme, only a designated verifier can verify the validity of a proxy signed message, which is suitable for many applications such as electronic voting (e-voting) and software licensing. On the basis of the requirements for actual applications, till now, many ID-DVPS schemes have been proposed. However, it has been found that most of existed ID-DVPS schemes have at least one of the following disadvantages: informal security proof, which makes these schemes vulnerable to attack, so they cannot be applied in practical environments; high computation and communication cost, which limits their practical applications especially in limited resource environments. In this paper, in order to obtain better properties of ID-DVPS scheme, we propose a novel ID-DVPS scheme. Compared with other existed ID-DVPS schemes, our scheme not only has lower computational cost but also has shorter signature size (only one element is needed for a signature). What is more, we present a formal definition of security model for ID-DVPS scheme and show a formal security proof of our new scheme based on the bilinear Diffie–Hellman assumption in the random oracle model. Additionally, we also present an instance of applying our ID-DVPS scheme to e-voting. Copyright © 2014 John Wiley & Sons, Ltd.