Using quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we prove the existence of bosonic edge states. For single-layer honeycomb lattices, bosonic edge states can be created, cross the gap, and merge into bulk states using an on-site potential applied to the outermost sites of the boundary. On the bilayer honeycomb lattice, bosonic edge states traversing the gap at half filling are demonstrated. The topological origin of the bosonic edge states is discussed in terms of the pseudo-Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states using ultracold bosons trapped in honeycomb optical lattices. Introduction.-Many important phenomena in condensed matter physics share the same intriguing feature, namely, the presence of edge states in the gap. Well-known examples include the quantum Hall effect (QHE), topological insulators, and graphene systems [1][2][3][4]. The appearance of an edge state is the consequence of the non-trivial topological properties of the bulk band. Edge states have been created in various systems such as quantum wells and graphene [5][6][7][8]; the existence of edge states constitutes a central motivation for studying these kinds of materials. Edge states are perfectly conducting channels and play an important role in electronic transport [9]. Edge states can be engineered to create onedimensional topological superconductors, which support localized Majorana fermions [10].