  In this work, we study the SM-like Higgs pair productions in the framework of
the general CP-violating two-Higgs-doublet model. Several constraints are
imposed to the model sequentially, including the SM-like Higgs boson signal
fits, the precise measurements of the electric dipole moments, the perturbative
unitarity and stability bounds to the Higgs potential, and the most recent LHC
searches for the heavy Higgs bosons. We show how are the CP-violating mixing
angles related to the Higgs cubic self couplings in this setup. Afterwards, we
estimate the cross sections of the future LHC/SppC searches for the Higgs pair
productions, as well as other possible decay modes for the heavy Higgs bosons.
