Leakage of private information including private keys of user has become a threat to the security of computing systems. It has become a common security requirement that a cryptographic scheme should withstand various leakage attacks. In the real life, an adversary can break the security of cryptography primitive by performing continuous leakage attacks. Although, some research on the leakage-resilient cryptography had been made, there are still some remaining issued in previous attempts. The identity-based encryption (IBE) constructions were designed in the bounded-leakage model, and might not be able to meet their claimed security under the continuous-leakage attacks. In the real applications, the leakage is unbounded. That is, a practical cryptography scheme should keep its original security in the continuous leakage setting. The previous continuous leakageresilient IBE schemes either only achieve chosen-plaintext attacks security or the chosen-ciphertext attacks (CCA) security is proved in the selective identity model. Aiming to solve these problems, in this paper, we show how to construct the continuous leakage-resilient IBE scheme, and the scheme’s adaptive CCA security is proved in the standard model based on the hardness of decisional bilinear Diffie-Hellman exponent assumption. For any adversary, all elements in the ciphertext are random, and an adversary cannot obtain any leakage on the private key of user from the corresponding given ciphertext. Moreover, the leakage parameter of our proposal is independent of the plaintext space and has a constant size.