With the advancement of medical science, the implementation of Electronic Medical Records (EMRs) for enhancing the efficiency and reliability of healthcare services has become a widespread phenomenon. However, EMRs are stored in hospitals and medical institutions independently, leading to sharing challenges. Moreover, the highly sensitive EMRs are prone to be tampered with and abused, posing privacy and security threats. To address the aforementioned issues, we propose an Anti- Quantum Attribute-based Signature(AQ - ABS) for Secure EMRs Sharing with Blockchain. Initially, We are the first ones to design an Attribute-based Signature (ABS) that can resist quantum attacks in E-health, called AQ - ABS. Further, the owner and provider of the EMR encrypt and sign it via the AQ - ABS scheme, then store EMR to a secure and distributed file storage system, i.e. Interplanetary File System (IPFS). Finally, the index hashes generated by IPFS and keywords are re-signed and stored in the consortium blockchain. Security analysis indicates that our proposed scheme fulfills the properties of signers' anonymity, EMRs unforgeability, EMRs shareability, and fine-grained access control. Comprehensive experimental evaluation demonstrates that our proposed scheme performs low overhead as well as outperforms existing ABS and EMR systems.