  Gluon fusion is the main production mechanism for Higgs bosons with masses up
to several hundred GeV in $pp$ collisions at the CERN Large Hadron Collider. We
investigate the effects of the CP-violating phases on the fusion process
including both the sfermion-loop contributions and the one-loop induced
CP-violating scalar-pseudoscalar mixing in the minimal supersymmetric standard
model. With a universal trilinear parameter assumed, every physical observable
involves only the sum of the phases of the universal trilinear parameter $A$
and the higgsino mass parameter $\mu$. The phase affects the lightest
Higgs-boson production rate significantly through the neutral Higgs-boson
mixing and, for the masses around the lightest stop-pair threshold, it also
changes the production rate of the heavy Higgs bosons significantly through
both the stop and sbottom loops and the neutral Higgs-boson mixing.
