Attribute-based encryption scheme is a scheme in which each user is identified by a set of attributes, and some function of those attributes is used to determine decryption ability for each ciphertext. Similar with identity-based encryption scheme, attribute-based schemes are also confronted with key escrow problem. Furthermore, the attributes belonging to a user usually are monitored by different authorities. This paper resolves the two problems by using a general attribute-based encryption scheme and K-Sibling intractable function families. In our construction, different attributes sets of a user are still certified by different authorities, but the partial private keys corresponding to the attributes are generated by a central authority. Simultineously, different authorities jointly generate the users’ secret value which cannot be obtained by the central authority. Compared with general multi-authourity attributed-based encryption scheme, our approach has more efficiency.