  The muon anomalous magnetic moment is investigated in the standard model with
two Higgs doublets (S2HDM) motivated from spontaneous CP violation. Thus all
the effective Yukawa couplings become complex. As a consequence of the non-zero
phase in the couplings, the one loop contribution from the neutral scalar
bosons could be positive and negative relying on the CP phases. The
interference between one and two loop diagrams can be constructive in a large
parameter space of CP-phases. This will result in a significant contribution to
muon anomalous magnetic moment even in the flavor conserving process with a
heavy neutral scalar boson ($m_h \sim$ 200 GeV) once the effective muon Yukawa
coupling is large ($|\xi_\mu|\sim 50$). In general, the one loop contributions
from lepton flavor changing scalar interactions become more important. In
particular, when all contributions are positive in a reasonable parameter space
of CP phases, the recently reported 2.6 sigma experiment vs. theory deviation
can be easily explained even for a heavy scalar boson with a relative small
Yukawa coupling in the S2HDM.
