  With the motivation of explaining the dark matter and achieving the
electroweak baryogenesis via the spontaneous CP-violation at high temperature,
we propose a complex singlet scalar ($S=\frac{\chi+i\eta_s}{\sqrt{2}}$)
extension of the two-Higgs-doublet model respecting a discrete dark
CP-symmetry: $S\to -S^*$. The dark CP-symmetry guarantees $\chi$ to be a dark
matter candidate on one hand and on the other hand allows $\eta_s$ to have
mixings with the pseudoscalars of the Higgs doublet fields, which play key
roles in generating the CP-violation sources needed by the electroweak
baryogenesis at high temperature. The universe undergoes multi-step phase
transitions, including a strongly first-order electroweak phase transition
during which the baryon number is produced. At the present temperature, the
observed vacuum is produced and the CP-symmetry is restored so that the
stringent electric dipole moment experimental bounds are satisfied. Considering
relevant constraints, we study the simple scenario of $m_{\chi}$ around the
Higgs resonance region, and find that the dark matter relic abundance and the
baryon asymmetry can be simultaneously explained. Finally, we briefly discuss
the gravitational wave signatures at future space-based detectors and the LHC
signatures.
