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A digital signature with designated verifier (SWDV) makes that only the designated verifier can verify its validity. It can be used to protect the privacy and economic interest of the signer. So, the SWDV schemes have many applications in e-voting, auction and some other fields. To make the SWDV secure against the quantum forger, a quantum signature with designated verifier signature (QSWDV) scheme is proposed. Our QSWDV is robust due to its strong security against forgery attack, inter-resending attacks, impersonation attacks and Trojan horse attacks. Its properties such as non-transferability and hiding source can be guaranteed by the signature simulation of the designated verifier. What is more, our scheme can be proved to be information-theoretically secure, which can guarantee the secrecy of the signer’s private key and the unforgeability of the QSWDV. In the proposed QSWDV scheme, the partners neither need use quantum one-way function nor need perform quantum state comparisons, which can reduce the complexity and improve the efficiency the QSWDV scheme.