Layered transition-metal chalcogenides (Zr,Hf)GeTe4 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)GeTe4 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 ZrGeTe4 and HfGeTe4 were 6.5 K under 57 GPa and 6.6 K under 60 GPa, respectively.