Layered transition-metal chalcogenides (Zr,Hf)GeTe$_{4}$ were screened out from database of Atomwork as a candidate for pressure-induced superconductivity due to their narrow band gap and high density of state near the Fermi level. The (Zr,Hf)GeTe$_{4}$ samples were synthesized in single crystal and then the compositional ratio, crystal structures, and valence states were investigated via energy dispersive spectrometry, single crystal X-ray diffraction, and X-ray photoelectron spectroscopy, respectively. The pressure-induced superconductivity in both crystals were first time reported by using a diamond anvil cell with a boron-doped diamond electrode and an undoped diamond insulating layer. The maximum superconducting transition temperatures of ZrGeTe$_{4}$ and HfGeTe$_{4}$ were 6.5 K under 57 GPa and 6.6 K under 60 GPa, respectively.
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