In this paper, we firstly present a MA-ABE scheme from lattices, in which identities of users are authenticated by a central authority, which improves the efficiency of authentication. Furthermore, different attribute private keys are still distributed by different authorities, and the central authority cannot obtain any secret information of other attribute authorities, which resolves key escrow problem to some extent. In MAABE, attribute private keys belonging to one user are generated by different authorities, and how to ensure correct decryption is one of the crux of schemes. Our scheme gives a simple solution, and each user's attribute private keys are combined using sharing of common public information to automatically realize correct decryption. To our best knowledge, this is the first MA-ABE scheme from lattices, and it is more efficient than the MA-ABE presented by Melissa Chase. Finally, we present a multi-authority large universe ABE scheme, in which the sizes of the public key and the ciphertext are only relative to the number of the attribute authorities, and a user will be able to decrypt a ciphertext if and only if he has at least tK attributes from each authority K.