Advances in quantum computers pose po-tential threats to the currently used public-key cryp-tographic algorithms such as RSA and ECC. As a promising candidate against attackers equipped with quantum computational power, Multivariate Public-Key Cryptosystems (MPKCs) has attracted increas-ing attention in recently years. Unfortunately, the existing MPKCs can only be used as multivariate signature schemes, and the way to construct an ef-ficient MPKC enabling secure encryption remains unknown. By employing the basic MQ-trapdoors, this paper proposes a novel multivariate encryption scheme by combining MPKCs and code-based pub-lic-key encryption schemes. Our new construction gives a positive response to the challenges in multi-variate public key cryptography. Thorough analysis shows that our scheme is secure and efficient, and its private key size is about 10 times smaller than that of McEliece-type cryptosystems.