Candidate compounds for new thermoelectric and superconducting materials, which have narrow band gap and flat bands near band edges, were exhaustively searched by the high-throughput first-principles calculation from an inorganic materials database named AtomWork. We focused on PbBi2Te4 which has the similar electronic band structure and the same crystal structure with those of a pressure-induced superconductor SnBi2Se4 explored by the same data-driven approach. The PbBi2Te4 was successfully synthesized as single crystals using a melt and slow cooling method. The core level X-ray photoelectron spectroscopy analysis revealed Pb2+, Bi3+ and Te2- valence states in PbBi2Te4. The thermoelectric properties of the PbBi2Te4 sample were measured at ambient pressure and the electrical resistance was also evaluated under high pressure using a diamond anvil cell with boron-doped diamond electrodes. The resistance decreased with increasing of the pressure, and pressure-induced superconducting transitions were discovered at 2.5 K under 10 GPa. The maximum superconducting transition temperature increased up to 8.4 K at 21.7 GPa. The data-driven approach shows promising power to accelerate the discovery of new thermoelectric and superconducting materials.