The topological edge states of two-dimensional topological insulators with large energy gaps fuish ideal conduction channels for dissipationless current transport.Transition metal tellurides X Te5 (X=Zr,Hf) are theoretically predicted to be large-gap two-dimensional topological insulators,and the experimental observations of their bulk insulating gap and in-gap edge states have been reported,but the topological nature of these edge states still remains to be further elucidated.Here,we report our low-temperature scanning tunneling microscopy/spectroscopy study on single crystals of HfTe5.We demonstrate a full energy gap of ～80meV near the Fermi level on the surface monolayer of HfTe5 and that such an insulating energy gap gets filled with finite energy states when measured at the monolayer step edges.Remarkably,such states are absent at the edges of a narrow monolayer strip of one-unit-cell in width but persist at both step edges of a unit-cell wide monolayer groove.These experimental observations strongly indicate that the edge states of HfTe5 monolayers are not trivially caused by translational symmetry breaking,instead they are topological in nature protected by the 2D nontrivial bulk properties.