  It is found that CP symmetry may be explicitly broken in the Higgs sector of
a supersymmetric $E_6$ model with two extra neutral gauge bosons at the
one-loop level. The phenomenology of the model, the Higgs sector in particular,
is studied for a reasonable parameter space of the model, in the presence of
explicit CP violation at the one-loop level. At least one of the neutral Higgs
bosons of the model might be produced via the $WW$ fusion process at the Large
Hadron Collider.
