Given that the existing quantum designated verifier signature schemes require the preparation of entanglement resources in advance and pose a risk of being attacked, a new quantum designated verifier signature scheme is designed in this work based on the quantum walk principle. The new protocol uses two coins quantum walking system on the complete graph,achieving quantum key generation and transmission of signature information. With the help of the trust center, the key generated by quantum walk is shared between the signer and the designated verifier in the new scheme, without the require to share the pre-keys and the entangled states. In the signature phase, the signer encrypts the message by using a key to perform controlled unitary operations, and the generated signature is sent to a designated verifier through quantum teleportation for verification, ensuring the integrity of the message and the correctness of the source. Furthermore, through the theoretical derivation of the examples and the simulation experiments on IBM quantum cloud platform, the correctness of the designed scheme is verified. The final security analysis shows that this scheme not only meets the requirements of designated verification, unforgeability, non-transferability and hiding source, but also is secure under entanglement attacks and intercept-and-resend attacks.