In this paper we propose a lattice-based anonymous broadcast encryption scheme obtained by translating the broadcast encryption scheme of Paterson et al. [7] into the lattices environment. We use two essential cryptographic primitives for our construction: tag-based hint systems secure under Ring-LWE hardness and IND-CCA secure cryptosystem under LWE-hardness. We show that it is feasible to construct anonymous tag-based hint systems from Ring-LWE problem for which we use a variant with ”small” secrets known to be as hard as regular Ring-LWE. We employ an IND-CCA-secure public key encryption scheme from LWE [12] for the PKE component of the anonymous broadcast encryption scheme.