In traditional public-key encryption schemes, security guarantees will be fully lost once decryption secret keys are exposed. With the ever-increase in encryption systems used in mobile and low secuirity devices, key exposure seems unavoidable. An intrusionresilient public-key encryption is proposed to mitigate the damage for the encryption systems brought by key exposure, which provides more security than the forward-secure encryption and key-insulated encryption. In its primitive, the whole lifetime is divided into discrete periods where the public key is fixed. Secret keys are shared in a decrypter and a base. The former performs the decrypting operations on his own while the latter provides an updated message to help evolve secret keys in each period. Furthermore, multiple operations of refresh secret keys are performed to refresh decrypter and base secrets periodically. The security can be preserved when both the user and base are compromised, as long as they are not compromised simultaneously. In addition, the simultaneous compromise doesn't affect the security of the ciphertext generated in previous periods. This paper proposes an intrusion-resilient public-key encryption scheme. All the parameters in this scheme have at most a log-squared complexity in terms of the total number of time periods. The proposed scheme is proven to be secure in the standard model and is a provably secure intrusion-resilient public-key encryption scheme without random oracles.