In this paper, we propose a new leakage-resilient identity-based encryption (IBE) scheme that is secure against chosen-ciphertext attacks (CCA) in the bounded memory leakage model. It is the first CCA-secure leakage-resilient IBE scheme which does not depend on $\mathtt{q}$-type assumptions. More precisely, it is secure under the DLIN and XDH assumption for symmetric and asymmetric bilinear groups, respectively. The leakage rate 1/6 is achieved under the XDH assumption.