In order to resist the forgery attack of weak blind signature, a double weak blind signature scheme is proposed based on the quantum entanglement swapping principle. The scheme is completed by initializing, message blindness, double blind signature and verification by the sender, signer and verifier. The sender sends message after the blind to the signer. The signer produces blind signature with quantum controlled Not gate and performs Bell state measurement. The sender performs signature on the original message again with quantum measurement. The verifier verifies the two signatures separately and removes the blind to restore the original message. If a participant disputes the results of signature verification, the dispute is arbitrated by a trusted signer. Analysis shows that when the even digit of the key is constant 1, the method can not only resist external attack, but also prevent the sender from tampering effectively. It satisfies the unforgeable, non-repudiation, blind and traceability requirements of weak blind signature. The proposed scheme has broad application prospect in electronic commerce, electronic currency and other internet transactions.