The file hierarchy ciphertext policy attribute-based encryption (FH-CP-ABE) scheme realizes multi-level files encryption with the single access policy, which saves the computation cost of encryption and decryption and the storage cost of ciphertext. Nevertheless, the existing file hierarchy CP-ABE scheme cannot support graded user access, while suffers due to the unauthorized access. For this reason, a file hierarchy CP-ABE scheme that supports graded user access is proposed. In the proposed scheme, the graded user access tree is constructed, and the ciphertext subsections are reconstructed to support the access requirements of graded users, thus eliminate the possibility of users to conduct unauthorized access. The security analysis shows that the proposed scheme can resist selective chosen-plaintext attack. Both theoretical and experimental analyses show that the proposed scheme is more efficient in terms of computation and storage compared to related scheme.