For leakage-resilient ciphertext-policy attribute-based encryption(CP-ABE) at present, the size of the ciphertexts in most of them relies on the number of attributes. How to overcome this shortcoming is a challenge problem. Based on the Goldreich-Levin theorem and dual system encryption, an efficient CP-ABE scheme with constant size ciphertexts is proposed in this paper. It can tolerate leakage on master secret key and attribute-based secret keys with auxiliary inputs. Furthermore, the proposed scheme can be realized as resilience against continual leakage if keys are periodically updated. Under some static assumptions instead of other strong assumptions, the introduced scheme achieves adaptively security in the standard model. For leakage-resilient ciphertext-policy attribute-based encryption (CP-ABE) at present, the size of the ciphertexts in most of them relies on the number of attributes. How to overcome this shortcoming is a challenge problem. Based on the Goldreich- Levin theorem and dual system encryption, an efficient CP-ABE scheme with constant size ciphertexts is proposed in this paper. Furthermore, the proposed scheme can be realized as resilience against continual leakage if keys are for now updated. Under some static assumptions instead of other strong assumptions, the introduced scheme achieves adaptively security in the standard model.