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.