We consider the problem of searchable encryption scheme for the cryptographic cloud storage in such a way that it can be efficiently and privately executed under the multi-user setting. Searchable encryption schemes allow users to perform keyword searches on encrypted files to retrieve their interested data without decryption. All existing such schemes only consider the straightforward search approach where for searching one encrypted keyword, the cloud server must look round all encrypted files on the storage to compare that encrypted keyword to each keyword index. Since the file number can be very huge and the user may be unable to decrypt all files, that approach is not efficient and secure enough. In this paper, we first propose a keyword search scheme for the cryptographic cloud storage based on attribute-based cryptosystems. Our scheme presents a new keyword search notion: fine-grained access control aware keyword search. By narrowing the search scope to the user's decryptable files' group before executing the keyword search, our approach can both decrease information leakage from the query process and be more efficient than other existing schemes.