  We explore the parameter regions in the complex Two Higgs Doublet Model
(c2HDM) with explicit CP violation that can describe current LHC hints for one
or more Higgs boson signals at 125 GeV. Such a simple extension of the Standard
model has three neutral Higgs bosons and a pair charged Higgs and leads to rich
CP-violating sources including the CP-even CP-odd mixing of the neutral Higgs
bosons. Within this model we present the production of light Higgs boson at the
LHC followed by its decay into two photons. Our numerical study takes into
account theoretical and experimental constraints on the Higgs potential like
positivity, unitarity and perturbativity as well as $\rho$-parameter, $b\to
s\gamma$ and $R_b$. These requirement together with the minimum conditions
could explain the di-photon excess observed at the LHC. We also discuss the
effects of the CP violating phases on the CP violation observable which is the
difference between left-circular and right-circular polarization.
