A strong designated verifier signature (SDVS) scheme only allows a designated verifier to validate signer’s signatures for ensuring confidentiality. At the same time, the designated verifier can not transfer the signature to any third party, since he can also generate another computationally indistinguishable SDVS, which is referred to as non-transferability. A proxy signature scheme is a special type of digital signature schemes, which enables an authorized proxy signer to create a valid proxy signature on behalf of the original one. The resulted proxy signature is publicly verifiable by anyone. In this paper, we elaborate on the merits of SDVS schemes and proxy signature schemes to propose an efficient strong designated verifier proxy signature (SDVPS) scheme in which only a designated verifier can be convinced of the proxy signer's identity. The proposed scheme has crucial benefits in organizational operations and electronic commerce. Compared with related schemes, ours has not only shorter signature length, but also lower computational costs. Moreover, the security requirement of unforgeability against existential forgery under adaptive chosen-message attacks (EF-CMA) is proved in the random oracle model.