Functional encryption provides more sophisticated and flexible relations between the encryption-key and decryption-key. Previous FE systems only allow for functionalities that take in a single authority key and plaintext as inputs. In this paper, a Multiple-Authority-Keys Attribute-Based Encryption system is presented. The new propose scheme allows descriptor to learn functionalities that take in a multiple authority keys and plaintext as inputs. The KGC with multiple authority keys can combine user's capabilities in a specified manner. We provide a proof of security in selective security model and collusion resistance. Furthermore, the performance of our new scheme compares favorably with single-authority-keys schemes.