The discovery of high-temperature superconductivity in La3Ni2O7 and La4Ni3O10 under pressure has garnered extensive attention. Herein, we report systematic investigations on the structure, magnetism, and electrical resistance evolutions of Pr4Ni3O10-delta polycrystalline samples under various pressures. Pr4Ni3O10-delta exhibits density wave transitions on Ni and Pr sublattices at approximately 157.6 and 4.3 K, respectively. The density wave can be progressively suppressed by pressure. A structural transformation from the monoclinic P21/a space group to the tetragonal I4/mmm occurs around 20 GPa. An apparent drop in resistance with an evident magnetic field dependence is observed at pressures above 20 GPa, indicating the emergence of superconductivity. The discovery of superconductivity in Pr4Ni3O10-delta broadens the family of nickelate superconductors. Pr4Ni3O10-delta provides a new platform for investigation of the mechanisms of superconductivity in the Ruddlesden-Popper phases of nickelates.