High‐entropy ceramics (HECs) are solid solutions of inorganic compounds with one or more Wyckoff sites shared by equal or near‐equal atomic ratios of multi‐principal elements. Material design and property tailoring possibilities emerge from this new class of materials. Herein, the discovery of superconductivity 2.35 K and topological properties in the (Ti0.2Zr0.2Nb0.2Hf0.2Ta0.2)C high‐entropy carbide ceramic (HECC) is reported, which is not observed before in any of the investigated HECC. Density functional theory calculations show that six type‐II Dirac points exist in (Ti0.2Zr0.2Nb0.2Hf0.2Ta0.2)C, which mainly contributed from the t2g orbitals of transition metals and the p orbitals of C. Due to the stability of the structure, robust superconductivity (SC) under pressure in this HEC superconductor is also observed. This study expands the physical properties of HECs, which may become a new material platform for SC research, especially for studying the coupling between SC and topological physics.