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Significant research effort has been devoted to searching for materials that host both superconducting and topological state, known as topological superconductor. Unfortunately, all the known topological superconductors to date have a very low transition temperature, which severely limits experimental measurement of Majorana fermions. We discover the existence of a topological Dirac-nodal-line (DNL) state in MgB₂ which has the highest transition temperature (~40 K) for a conventional BCS superconductor using first-principles calculations. The DNL structure in MgB₂ exhibits unique one-dimensional dispersive DNL, which connects the electron and hole Dirac states. Since the experimental samples and superconductivity measurement of MgB₂ is well established, confirmation of our theoretical prediction is highly feasible.