The invention discloses a quantum attack resistant asymmetric encryption method based on a ffinite groups of lie type. The method comprises the following steps that: a key generation center generatesa system main public-private key pair; and then, in the encryption stage, the encryption party A encrypts the message m by using the public key to obtain a ciphertext C; and finally, in the decryptionstage, the receiver decrypts the ciphertext C by using the private key to obtain a message m. The basic realization platform is a finite groups of lie type, can reach IND- CCA safety required by a classic public key cryptosystem, and has the capability of resisting the attack of the existing quantum algorithm.