A Dirac fermion in a topological Dirac semimetal is a quadruple-degenerate quasiparticle state with a relativistic linear dispersion. Breaking either time-reversal or inversion symmetry turns this system into a Weyl semimetal that hosts double-degenerate Weyl fermion states with opposite chiralities. These two kinds of quasiparticles, although described by a relativistic Dirac equation, do not necessarily obey Lorentz invariance, allowing the existence of so-called type-II fermions. The recent theoretical discovery of type-II Weyl fermions evokes the prediction of type-II Dirac fermions in PtSe_{2}-type transition metal dichalcogenides, expecting experimental confirmation. Here, we report an experimental realization of type-II Dirac fermions in PdTe_{2} by angle-resolved photoemission spectroscopy combined with ab initio band calculations. Our experimental finding shows the first example that has both superconductivity and type-II Dirac fermions, which turns the topological material research into a new phase.