Tungsten ditelluride has attracted intense research interest due to the recent discovery of its large unsaturated magnetoresistance up to 60 T. Motivated by the presence of a small, sensitive Fermi surface of 5d electronic orbitals, we boost the electronic properties by applying a high pressure, and introduce superconductivity successfully. Superconductivity sharply appears at a pressure of 2.5 GPa, rapidly reaching a maximum critical temperature (Tc) of 7 K at around 16.8 GPa, followed by a monotonic decrease in Tc with increasing pressure, thereby exhibiting the typical dome-shaped superconducting phase. From theoretical calculations, we interpret the low-pressure region of the superconducting dome to an enrichment of the density of states at the Fermi level and attribute the high-pressure decrease in Tc to possible structural instability. Thus, tungsten ditelluride may provide a new platform for our understanding of superconductivity phenomena in transition metal dichalcogenides.