Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analogue of graphene, have lately generated widespread interest in both materials science and condensed matter physics(1,2). Recently, crystalline Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atmosphere(3-9). Here, by using point contact spectroscopy measurements, we observe exotic superconductivity around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric around zero bias suggest p-wave-like unconventional superconductivity. Considering the topological properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topological superconductors(10-13), which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material(14-17).