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. Gornicka 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.
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