  Three-dimensional Dirac and Weyl semimetals have attracted widespread
interest in condensed matter physics and material science. Here, based on
first-principles calculations and symmetry analysis, we report that Ag$_2$S
with P2$_1$2$_1$2$_1$ symmetry is a topological Dirac semimetal in the absence
of spin-orbit coupling (SOC). Every Dirac points are composed of two Weyl
points with the same chirality overlapping in the momentum space. After taking
the SOC into consideration, each Dirac point is split into two Weyl points. The
Weyl points with the opposite chirality are far from each other in the momentum
space. Therefore, the Weyl pairs are not easy to annihilate and robust in the
Ag$_2$S compound, which also lead to long Fermi-arcs on material surface. The
robustness of the Weyl points against the strain is discussed.
