  The electric dipole moment is examined in a three-loop neutrino mass model
with dark matter originally proposed in Aoki et al. [Phys. Rev. Lett. 102,
051805 (2009)]. The model contains a $CP$-violating phase in the Higgs
potential which plays an important role in electroweak baryogenesis and is thus
expected to explain the baryon asymmetry of the Universe simultaneously.
However, such a $CP$-violating phase is severely constrained by the
measurements of the electron electric dipole moment (eEDM), and a suppression
mechanism for the eEDM is necessary to explain the observed baryon asymmetry
while avoiding the constraint. In this paper, we examine neutrino mass,
lepton-flavor-violating processes, dark matter, and the eEDM in the model. We
show that the eEDM can be suppressed by destructive interference between the
$CP$-violating phases in the Higgs sector and the dark sector with large
$CP$-violating phases. We propose some benchmark scenarios including $O(1)$
$CP$-violating phases where tiny neutrino mass and dark matter can be explained
while avoiding all current experimental and theoretical constraints. These
$CP$-violating phases are expected to be large enough to generate the observed
baryon asymmetry in the electroweak baryogenesis scenario.
