  We propose semi-direct Gauge-Yukawa mediation of supersymmetry (SUSY)
breaking. The messenger fields mediating SUSY breaking to the visible sector do
not directly couple with the goldstino field, and instead they have gauge and
Yukawa interactions with some primary messenger fields which couple directly
with the goldstino fields. From the explicit Feynman diagram calculations for
the SUSY breaking soft masses, we find that the SUSY particle spectra can be
realistic. Especially, this generalization of semi-direct gauge mediation
solves the massless gaugino mass problem since the holomorphic soft mass terms
of the messenger fields can be generated by Yukawa couplings. We also provide
some arguments that this scenario can be realized naturally in some dynamical
SUSY-breaking models such as the ISS-like model.
