In this paper, we construct the first efficient leakageresilient CCA2 (LR-CCA2)-secure attribute-based encryption (ABE) schemes. We also construct the first efficient LR-CCA2-secure identitybased encryption (IBE) scheme with optimal leakage rate.To obtain our results, we develop a new quasi-adaptive non-interactive zero-knowledge (QA-NIZK) argument for the ciphertext consistency of the LR-CPA-secure schemes.Our ABE schemes are obtained by boosting the LR-CPA-security of some existing schemes to the LR-CCA2-security by using our QA-NIZK arguments. The schemes are almost as efficient as the underlying LR-CPAsecure schemes.