Strong designated verifier signatures (SDVS) allows users to produce signatures that are not publicly verifiable, such that no one other than the signer and the designated verifier can check the validity of a given signature, which preserves the privacy of the signer. This cryptographic primitive is very useful in different real life scenarios such as e-voting and e-bidding. In this paper, we propose a strong designated verifier signature scheme (SDVS) based on rank metric error correcting codes. Our construction makes a trade-off between efficiency and security requirements, for instance we achieve a signature of size 3510 bits and a public key of size equal to 23088 bits for the 80 security level. Furthermore, our proposal is quantum computer resistant since it is based on coding theory.