We report the discovery of superconductivity on the border of long-range magnetic order in the itinerant-electron helimagnet MnP via the application of high pressure. Superconductivity with T(sc)≈1 K emerges and exists merely near the critical pressure P(c)≈8 GPa, where the long-range magnetic order just vanishes. The present finding makes MnP the first Mn-based superconductor. The close proximity of superconductivity to a magnetic instability suggests an unconventional pairing mechanism. Moreover, the detailed analysis of the normal-state transport properties evidenced non-Fermi-liquid behavior and the dramatic enhancement of the quasiparticle effective mass near P(c) associated with the magnetic quantum fluctuations.