Alwen et al. in Eurocrypt 2010, showed that an identity-based hash proof system (IB-HPS), where IB-HPS generalizes the notion of hash proof system (HPS) to the identity-based setting, almost immediately yields an identity-based encryption (IBE) scheme which is secure against partial leakage of the target identity's decryption key. That is, an IBE scheme with bounded leakage resilience can be naturally created from an IB-HPS. However, in the real world, the leakage is unbounded, and any adversary can break the security of cryptography shceme by performing continuous leakage attacks. To further increase the practicability, a cryptography scheme must hold the claimed security in the continuous leakage setting. Dodis et al. in FOCS 2010, showed a generic method how to create a cryptography shceme with continuous leakage resilience from the bounded leakage-resilient cryptosystem by performing an additional key update algorithm while the public parameters keep unchanged. To construct a continuous leakage-resilient cryptography scheme, a new primitive, called it updatable identity-based hash proof system (U-IB-HPS), is proposed, which is an improved IB-HPS. In particular, the improved system has an additional key update algorithm, which can push some new randomness into the private key of user (or the master secret key), the updated results are random in the adversary's view, and the leakage of previous private key of user (or the master secret key) does not work for the updated results. However, the previous instantiations of U-IB-HPS cannot achieve the claimed security. To solve the above problems, in this paper, two instantiations of U-IB-HPS with better performance are created, and the security of proposed system is proved, in the standard model, based on the classic decisional bilinear Diffie-Hellman assumption. The corresponding IBE scheme created with our U-IB-HPS allows continuous leakage of multiple keys, i.e., continuous leakage of the master secret key and the private key of user. Additionally, our U-IB-HPS can also be employed as an underlying basic tool to build the generic construction of continuous leakage-amplified public-key encryption scheme, continuous leakage-resilient identity-based authenticated key exchange protocol, and continuous leakage-resilient public-key encryption scheme with keyword search, etc.