An extended study on PdS is carried out with the measurements of the resistivity, Hall coefficient, Raman scattering, and x-ray diffraction at high pressures up to 42.3 GPa. With increasing pressure, superconductivity is observed accompanying with a structural phase transition at around 19.5 GPa. The coexistence of semiconducting and metallic phases observed at normal state is examined by the Raman scattering and x-ray diffraction between 19.5 and 29.5 GPa. After that, only the metallic normal state maintains with an almost constant superconducting transition temperature. The similar evolution between the superconducting transition temperature and carrier concentration with pressure supports the phonon-mediated superconductivity in this material. These results highlight the important role of pressure played in inducing superconductivity from these narrow band-gap semiconductors.