The TaAs family (NbAs, TaAs, NbP, TaP) are kinds of Weyl semimetals with lots of novel properties, thus attracting considerable attention in recent years. Here, we systematically studied the Weyl semimetal NbP up to 72 GPa through the resistivity, Raman spectra, X-ray diffraction measurements, and first-principles density functional theory (DFT) calculations. A pressure-induced semimetal-metal transition was observed at ∼36 GPa, which was further confirmed by the DFT calculations. With further compression up to 52 GPa, a superconducting state was observed. Interestingly, the Tc increases significantly upon decompression and shows a dome-shaped trend as a function of pressure. Surprisingly, the pressure-induced superconductivity can be quenched to ambient pressure, and all transitions under pressure do not involve any structural change. Our work not only depicts a phase diagram of the NbP system under high pressure but also provides a new experimental insight for superconductivity in Weyl semimetals.