  We discuss the singlet-doublet fermion dark matter model with CP-violation.
In this model, the CP-violation generates a pseudo-scalar interaction of dark
matter with the SM-Higgs boson. Thanks to the pseudo-scalar interaction, the
model can evade the strong constraint from the dark matter direct detection
experiments while keeping the success of the thermal relic scenario. The
CP-violation also predicts signals in dark matter indirect detection
experiments and electric dipole moments (EDM) that can be as large as the
current upper bound. We investigate the constraints and prospects of the direct
detection experiments, the indirect detection experiment, and the electron EDM.
We also investigate the stability of the Higgs potential. Combining these
observables, we find that heavy dark matter is disfavored. We also find it is
possible to probe the Higgs funnel region by the combination of the direct
detection experiments and the measurements of the electron EDM if experiments
for the electron EDM reach to $O(10^{ -32})$ e cm in future.
