  A recent experiment reported two new non-centrosymmetric superconductors
NbIr$_{2}$B$_{2}$ and TaIr$_{2}$B$_{2}$ with respective superconducting
transition temperatures of 7.2 K and 5.2 K and further suggested their
superconductivity to be unconventional [K. G\'ornicka \textit{et al}., Adv.
Funct. Mater. 2007960 (2020)]. Here, based on first-principles calculations and
symmetry analysis, we propose that $T$Ir$_{2}$B$_{2}$ ($T$=Nb, Ta) are
topological Weyl metals in the normal state. In the absence of spin-orbit
coupling (SOC), we find that NbIr$_{2}$B$_{2}$ has 12 Weyl points, and
TaIr$_{2}$B$_{2}$ has 4 Weyl points, i.e. the minimum number under
time-reversal symmetry; meanwhile, both of them have a nodal net composed of
three nodal lines. In the presence of SOC, a nodal loop on the mirror plane
evolves into two hourglass Weyl rings, along with the Weyl points, which are
dictated by the nonsymmorphic glide mirror symmetry. Besides the rings,
NbIr$_{2}$B$_{2}$ and TaIr$_{2}$B$_{2}$ have 16 and 20 pairs of Weyl points,
respectively. The surface Fermi arcs are explicitly demonstrated. On the (110)
surface of TaIr$_{2}$B$_{2}$, we find extremely long surface Fermi arcs
($\sim$0.6 ${\text{\AA}}^{-1}$) located 1.4 meV below the Fermi level, which
should be readily probed in experiment. Combined with the intrinsic
superconductivity and the nontrivial bulk Fermi surfaces, $T$Ir$_{2}$B$_{2}$
may thus provide a very promising platform to explore the three-dimensional
topological superconductivity.
