  We study the CP domain walls and the consequent gravitational waves induced
by the spontaneous breaking of the CP symmetry in the complex singlet extension
to the Standard Model. We impose the constraints from the unitarity, stability
and the global minimal of the vacuum solutions on the model parameter space.
The CP domain wall profiles and tensions are obtained by numerically solving
the relevant field equations. The explicit CP violation terms are then
introduced to the potential as biased terms to make the domain walls unstable
and collapse, The BBN bound on the magnitude of the energy bias is taken into
account. To achieve sufficiently strong gravitational wave signals, the domain
wall tension $\sigma$ is required to be at least $\sigma/{\rm TeV}^3 \sim
\mathcal{O}(10^3)$. We find that the gravitational wave spectrum can be probed
in the future SKA and/or DECIGO programs, when the typical mass scale is at
least $\sim \mathcal{O}(10)$ TeV and the explicit CP violation terms are as
small as $\mathcal{O}(10^{-29}) - \mathcal{O}(10^{-27}) $. The gravitational
waves from collapsing domain walls thus provide a complementarity to the probe
of extremely small CP violation at high-energy scale.
