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 × 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 HEPfit to perform a global parameter fit. We find that the decays of the two lightest extra neutral (singly-charged) scalars, H 1 and $H_2\left(H_1^{\pm }\right)$ $$ {H}_2\left({H}_1^{\pm}\right) $$ , 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.