  We study a pseudoscalar dark-matter model arising from a complex singlet
extension of the standard model (SM), and show that the dark-matter--nucleon
scattering is suppressed when two CP-even scalars are degenerate. In such a
degenerate-scalar scenario we explore the model parameter space which satisfies
constraints from the direct detection experiments and the relic density of dark
matter. In addition, we discuss a possibility to verify such a scenario by
using the recoil mass technique at the International Linear Collider. We find
that a pair of states separated by 0.2 GeV can be distinguished from the single
SM-like Higgs state at 5$\sigma$ with integrated luminosity of 2 ab$^{-1}$.
