Orthorhombic (space group: Pnma) Nb2P5 is a high-pressure phase that is quenchable to ambient pressure, which could viewed as the zigzag infinite P chain-inserted NbP2. We report herein the high-pressure crystal growth of Nb2P5 and the discovery of its superconducting transition at Tc ~ 2.6 K. The electrical resistivity, magnetization, and specific heat capacity measurements on the high-quality crystal unveiled a conventional type-II weakly coupled s-wave nature of the superconductivity, with the upper critical field Hc2(0) ~ 0.5 T, the electron-phonon coupling strength {lambda}ep ~ 0.5 - 0.8, and the Ginzburg-Landau parameter k{appa} ~ 100. The ab initio calculations on the electronic band structure unveiled nodal-line structures protected by different symmetries. The one caused by band inversion, for example, on the {Gamma}-X and U-R paths of the Brillouin zone, likely could bring nontrivial topology and hence possible nontrivial surface state on the surface. The surface states on the (100), (010) and (110) surfaces were also calculated and discussed. The discovery of the phosphorus-rich Nb2P5 superconductor would be instructive for the design of more metal phosphides superconductors which might host unconventional superconductivity or potential technical applications.