As the electronic commerce increases rapidly in the mobile communication, security issues become more important. A suitable authentication and key agreement for the mobile communication environment is a essential condition. Some protocols based on the public key cryptosystem such as Diffie-Hellman, EIGamal etc. were adapted in the mobile communication. But these protocols that are based on the difficult mathematical problem in the algebra, are so slow and have long key-length. Therefore, these have many limitation to apply to the mobile communication. In this paper, we propose an authentication and key agreement protocol based on NTRU to overcome the restriction of the mobile communication environment such as limited sources. low computational fewer, and narrow bandwidth. The proposed protocol is faster than other protocols based on ECC, because of addition and shift operation with small numbers in the truncated polynomial ring. And it is as secure as other existent mathematical problem because it is based on finding the Shortest or Closest Vector Problem(SVP/CVP).