As the simplest iron-based superconductor, FeSe forms a tetragonal structure with transition temperature Tc ~ 8 K. With assistance of pressure, or other techniques, Tc can be greatly enhanced, even to above liquid nitrogen temperature. The newly discovered superconducting tetragonal FeS (Tc ~ 4.5 K), a sulfide counterpart of FeSe, promotes us on its high pressure investigation. The transport and structure evolution of FeS with pressure have been studied. A rapid suppression of Tc and vanishing of superconductivity at 4.0 GPa are observed, followed by a second superconducting dome with a 30% enhancement in maximum Tc. An onsite tetragonal to hexagonal phase transition occurs around 7.0 GPa, followed by a broad pressure range of phase coexistence. The residual deformed tetragonal phase is considered as the source of second superconducting dome. The observation of two superconducting domes in iron-based superconductors poses great challenges for understanding their pairing mechanism.