A quantum authentication protocol is presented in this paper. It is based on the correlations of the EPR(Einstain-Podolski-Rosen) pair which is a two-qubit system in one of the four Bell states. The two parties share a sequence of EPR pairs as the authentication key. To authenticate each other, they need to create auxiliary particles and make them interact with the authentication key. Then one can affirm the other's identity by performing the Bell states measurement. No one without the authentication key can pass the authentication process. So the protocol is secure. No classical channel and classical information exchange is needed in the authentication process. After the authentication process, the authentication key can be turned into the origin state. So the authentication key can be reused.