 Abstract here, we propose a quantum asymmetric key cryptography scheme using Grover's quantum search algorithm. In the proposed scheme, Alice generates a pair of public and private keys, keeps the private key safe, and only discloses public keys to the outside. Bob uses Alice's public key to send a secret message to Alice and Alice uses her private key to decrypt the secret message. Furthermore, we discuss the safety of quantum asymmetric key encryption techniques based on quantum mechanical properties. This article was authored by Chang Sik Yoon, Chang Ho Hong, Min It Sung Kang, and others.