Two noncentrosymmetric ternary pnictides, CaAgP and CaAgAs, are reported as topological line-node semimetals protected solely by mirror-reflection symmetry. The band gap vanishes on a circle in momentum space, and surface states emerge within the circle. Extending this study to spin–orbit coupled systems reveals that, compared with CaAgP, a substantial band gap is induced in CaAgAs by large spin–orbit interaction. The resulting states are a topological insulator, in which the Z₂ topological invariant is given by 1;000. To clarify the Z₂ topological invariants for time-reversal-invariant systems without spatial-inversion symmetry, we introduce an alternative way to calculate the invariants characterizing a line node and topological insulator for mirror-reflection-invariant systems.