Abstract: A new certificateless signcryption scheme without using the bilinear pairings was presented based Discrete-Logarithm firstly,which was proved security in the random oracle model.Secondly,with the proposes signcryption scheme Canetti-Krawczyk model,the author proposes an efficient certificateless authentication and key exchange protocol without pairings.The security analysis of the proposed protocol in the implementation plan with the Canetti-Krawczyk model is presented in this paper.The results show that the proposed protocol is session-key secure with perfect forward secrecy.Moreover,the implementation of the protocol is just 1 encryption operation,3 exponent operations and twice communications.