In recent years, much attention has been focused on designing provably secure cryptographic primitives in the presence of key leakage. Many constructions of leakage-resilient cryptographic primitives have been proposed. However, for any polynomial time adversary, most existing leakage-resilient cryptographic primitives cannot ensure that their outputs are random, and any polynomial time adversary can obtain a certain amount of leakage on the secret key from the corresponding output of a cryptographic primitive. In this study, to achieve better performance, a new construction of a chosen ciphertext attack 2 (CCA2) secure, leakage-resilient, and certifi cateless public-key encryption scheme is proposed, whose security is proved based on the hardness of the classic decisional Diffie-Hellman assumption. According to our analysis, our method can tolerate leakage attacks on the private key. This method also achieves better performance because polynomial time adversaries cannot achieve leakage on the private key from the corresponding ciphertext, and a key leakage ratio of 1/2 can be achieved. Because of these good features, our method may be signifi cant in practical applications.