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The quasi-one-dimensional material PdTeI exhibits unusual electronic transport properties at ambient pressure. Here, we systematically investigate both the structural and electronic responses of PdTeI to external pressure, through a combination of electrical transport, synchrotron X-ray diffraction (XRD), and Raman spectroscopy measurements. The charge density wave (CDW) order in PdTeI is fragile and the transition temperature <i>T</i>_CDW decreases rapidly with the application of external pressure. The resistivity hump is indiscernible when the pressure is increased to ~1 GPa. Upon further compression, the resistivity dropping is observed approximately ~15 GPa and zero resistance is established above ~20 GPa, suggesting the occurrence of superconductivity. Combined XRD and Raman data evidence that the emergence of superconductivity is accompanied by a pressure-induced amorphization of PdTeI.