We report the discovery of a bulk superconducting transition at 3.4 K in the ternary phosphide, ScIrP, which crystallizes in a hexagonal ZrNiAl-type structure without spatial inversion symmetry. On the basis of heat capacity data in a zero magnetic field, ScIrP is suggested to be a weakly-coupled Bardeen-Cooper-Schrieffer superconductor. Alternatively, experimental results under magnetic fields indicate that this material is a type-II superconductor with an upper critical field H c2 at magnetic fields above 5 T at zero temperature. This moderately high H c2 does not violate the Pauli limit, but it does imply that there is a significant effect from the strong spin-orbit interaction of Ir 5d electrons in the noncentrosymmetric crystal structure. Electronic structure calculations show an interesting feature of ScIrP, where both the Sc 3d and Ir 5d orbitals contribute to the electronic density of states at the Fermi level.Elemental Ca and Sc show superconductivity with a relatively high transition temperature T c of ~20 K at high pressures. Ca is not a superconductor at ambient pressure but becomes superconducting above ~50 GPa [1]. T c increases with increasing pressure and exceeds 20 K at ~100 GPa [2], which is the highest T c in all elemental metals. Sc exhibits a superconducting transition above ~60 GPa, which approaches 20 K at 107 GPa [3,4]. At higher pressures, however, Sc undergoes a structural phase transition to a nonsuperconducting phase (Sc-III). If this transition did not occur, Sc would exhibit a T c higher than 20 K. In simple-metal superconductors such as Al, Sn, and Pb, T c decreases with increasing pressure due to a decrease of the electronic density of states (DOS). The pressure effects on T c in Ca and Sc, opposite to those in simple metals, have been discussed in terms of the pressure-induced s−d electron transfer where 4s electrons are dominant for electron conduction at ambient pressure and are transferred to the narrower 3d band by applying pressure [4,5]. The electrons occupying the 3d band play an important role in relatively high T c superconductivity.