We report the discovery of a new three-dimensional (3D) topological Dirac semimetal (TDS) material KZnBi, coexisting with a naturally formed superconducting state on the surface under ambient pressure. Using photoemission spectroscopy together with first-principles calculations, a 3D Dirac state with linear band dispersion is identified. The characteristic features of massless Dirac fermions are also confirmed by magnetotransport measurements, exhibiting an extremely small cyclotron mass of m* = 0.012 m(0) and a high Fermi velocity of V-F = 1.04 x 10(6) m/s. Interestingly, superconductivity occurs below 0.85 K on the (001) surface, while the bulk remains nonsuperconducting. The captured linear temperature dependence of the upper critical field suggests the possible non-s-wave character of this surface superconductivity. Our discovery serves a distinctive platform to study the interplay between 3D TDS and the superconductivity.