Ring signature provides perfect anonymity when a specific person from a set of possible signers signs on a document. So, it plays a very important role in leaking secrets and making decisions anonymously. By introducing the convertibility property, the actual signer can disclose his identity by releasing a secret value. In order to fit some real-life applications, it is advantageous to use convertibility property with ring signatures. Herein, we propose an advanced post-quantum convertible ring signature scheme. We construct our scheme using multivariate public-key cryptography, which is a useful weapon against quantum-equipped adversaries. Our proposed scheme consists of all the required security requisites, such as signer anonymity, unforgeability, and non-usurpability.