  The analogues of elementary particles have been extensively searched for in
condensed matter systems because of both scientific interests and technological
applications. Recently massless Dirac fermions were found to emerge as low
energy excitations in the materials named Dirac semimetals. All the currently
known Dirac semimetals are nonmagnetic with both time-reversal symmetry
$\mathcal{T}$ and inversion symmetry $\mathcal{P}$. Here we show that Dirac
fermions can exist in one type of antiferromagnetic systems, where
$\mathcal{T}$ and $\mathcal{P}$ are broken but their combination $\mathcal{PT}$
is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate,
analyze the robustness of the Dirac points with symmetry protections, and
demonstrate its distinctive bulk dispersions as well as the corresponding
surface states by \emph{ab initio} calculations. Our results give a new route
towards the realization of Dirac materials, and provide a possible platform to
study the interplay of Dirac fermion physics and magnetism.
