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Quantum spin Hall (QSH) insulators, a new class of quantum matter, can support topologically protected helical edge modes inside a bulk insulating gap, which can lead to dissipationless transport. A major obstacle to reaching a wide application of QSH is the lack of suitable QSH compounds, which should be easily fabricated and have a large bulk gap. Here, we predict that single-layer ZrTe_{5} and HfTe_{5} are the most promising candidates for large-gap insulators, with a bulk direct (indirect) band gap as large as 0.4 eV (0.1 eV) and which are robust against external strains. The three-dimensional crystals of these two materials are good layered compounds with very weak interlayer bonding, and they are located near the phase boundary between weak and strong topological insulators, paving a new way for future experimental studies on both the QSH effect and topological phase transitions.