  We discuss CP-violation in a model with a real and a complex isospin triplet
Higgs fields without introducing any symmetries except for the electroweak
gauge symmetry. This corresponds to the minimal extension of the Higgs sector
with the following properties: (i) providing new source of CP violation, (ii)
absence of quark flavor changing neutral currents at tree level, and (iii)
enabling the electroweak rho parameter to be unity at tree level in the
scenario without imposing any new symmetries. Our model can be regarded as the
generalized version of the Georgi-Machacek model, in which the global
$SU(2)_L\times SU(2)_R$ symmetry is explicitly broken due to CP-violating terms
in the potential. We present analytic formulas for theoretical constraints from
perturbative unitarity and vacuum stability as well as contributions to the
electron electric dipole moment (EDM) and the neutron EDM from all the Barr-Zee
type diagrams. We then examine the parameter space allowed by the constraints
mentioned above and also those from the uniqueness of the vacuum, measurements
at Tevatron and LHC by using \texttt{HEPfit} to perform a global parameter fit.
We find that the decays of the two lightest extra neutral (singly-charged)
scalars, $H_1$ and $H_2$ ($H_1^\pm$), into $hZ$ ($WZ$) can be significant at
the same time under the constraints, which can serve as direct evidence of CP
violation in our model, but not from models with multi-doublet extensions.
