  We study the domain wall solutions in the general two-Higgs-doublet model
(2HDM) with a CP-violating phase. The 2HDM with the spontaneouse CP violation
is found to have domain wall solutions whose tensions are
$\mathcal{O}(10^6)\,{\rm GeV}^3$, which are excluded by the
Zel'dovich-Kobzarev-Okun bound. With the explicit CP-violating (CPV) terms as
the so-called biased term in the scalar potential, domain walls can collapse in
the early Universe. The sizes of the explicit CP violation can be constrained
from the Big Bang nucleosynthesis. This constraint is converted to the CPV
mixing of $\alpha_c$, and is mostly sensitive to the mass splittings between
two heavy neutral Higgs bosons. We estimate the possible gravitational wave
signals and the electric dipole moment (EDM) predictions due to the domain wall
collapsing. It turns out that the peak spectrum of the GW from the domain wall
collapsing cannot be probed in any future program. In contrast, the untenable
regions with very tiny explicit CPV parameter in the Higgs potential has been
partially excluded by the latest electron EDM measurements at the ACME-II and
will be further confirmed or excluded by the future ACME-III projection.
