  Topological superconductors are an intriguing and elusive quantum phase,
characterized by topologically protected gapless surface/edge states residing
in a bulk superconducting gap, which hosts Majorana fermions. Unfortunately,
all currently known topological superconductors have a very low transition
temperature, limiting experimental measurements of Majorana fermions. Here we
discover the existence of a topological Dirac-nodal-line state in a well-known
conventional high-temperature superconductor, MgB2. First-principles
calculations show that the Dirac-nodal-line structure exhibits a unique
one-dimensional dispersive Dirac-nodal line, protected by both
spatial-inversion and time-reversal symmetry, which connects the electron and
hole Dirac states. Most importantly, we show that the topological
superconducting phase can be realized with a conventional s-wave
superconducting gap, evidenced by the topological edge mode of the MgB2 thin
films showing chiral edge states. Our discovery may enable the experimental
measurement of Majorana fermions at high temperature.
