Designated verifier signature (DVS) schemes can be applied in many scenes, such as E-voting and E-bidding using DVS attributes to protect the secret of participants. Most traditional DVS schemes are vulnerable to quantum computer attacks. Then, an identity-based semi-trusted third-party quantum DVS (STQDVS) scheme is proposed, which is safe for quantum means of attack. In the new STQDVS scheme, the third participant prepares entangled Bell states and allocates them to the signer and the designated verifier (DV). The signer uses the identity information as her public key and the measurement results of corresponding quantum sequences as her private key to generate the signature. The DV applies the identity information as his public key and the measurement results of corresponding quantum sequences as her private key to verify the signature. Non-transferability and hidden origin are guaranteed by the fact that the DV can generate the same signature as the signatory by means of a simulated signature step. Security analysis has shown that attacks such as forgery, inter-resending, and impersonation are ineffective for the proposed scheme and that even third-party cannot forge signatures. On the other hand, the whole process of the scheme does not require any quantum key distribution protocols, quantum one-way functions, and quantum state exchange tests, which makes the STQDVS scheme relatively simple and more efficient than similar schemes.