The invention discloses a novel on-lattice MA-ABE (Multi-Authority Attribute Based Encryption) method based on LWE, which comprises four steps of system initialization, secret key generation, encryption and decryption. According to the invention, a plurality of attribute mechanisms manage different attribute sets and respectively distribute secret keys to users in permissions of the attribute mechanisms so as to improve integral efficiency of a system when ensuring security; and meanwhile, a Shamir threshold secret sharing technology is applied, three operations of an access strategy, i.e., anAND operation, an OR operation and a threshold operation, are implemented by adopting an access tree structure, and flexibility is high. Moreover, according to the invention, bilinear pairing is replaced with a lattice principle, a lattice basis delegation algorithm without dimension growth is introduced, encryption and decryption speeds are improved, and storage cost of private keys and ciphertexts of users is reduced. The novel on-lattice MA-ABE method disclosed by the invention is comprehensive in consideration, perfect in function, optimal in system performance and can be better applied to a cloud storage environment.