This paper firstly provides the extended Canetti-Krawzcyk (eCK) security model for predicate-based authenticated key exchange (AKE) that guarantees resistance to leakage of ephemeral secret keys. Moreover, we propose two-pass key-policy (resp. session-policy) attribute-based AKE protocol secure in the proposed predicate-based eCK security model based on key-policy (resp. ciphertext-policy) attribute-based encryption. The proposed protocols have advantages in security against leakage of ephemeral secret keys and the round complexity compared to the previous predicate-based AKE protocols.