The discovery of superconducting states in diverse topological materials generates a burgeoning interest to explore a topological superconductor and to realize a fault-tolerant topological quantum computation. A variety of routes to realize topological superconductors are proposed, and many types of topological materials are developed. However, a pristine topological material with a natural superconducting state is relatively rare as compared to topological materials with artificially induced superconductivity. Here, it is reported that the planar honeycomb structured 3D topological Dirac semimetal (TDS) SrCuBi, which is the Zintl phase, shows a natural surface superconductivity at 2.1 K under ambient pressure. It is clearly identified from theoretical calculations that a topologically nontrivial state exists on the (100) surface. Further, its superconducting transition temperature (T<sub>c</sub>) increases by applying pressure, exhibiting a maximal T<sub>c</sub> of 4.8 K under 6.2 GPa. It is believed that this discovery opens up a new possibility of exploring exotic Majorana fermions at the surface of 3D TDS superconductors.