  We consider low scale gauge mediation models with a very light gravitino
m_{3/2}~16 eV, in the light of recent experimental hints on the Higgs boson
mass. The light gravitino is very interesting since there is no gravitino
over-production problem, but it seems difficult to explain the Higgs boson mass
of ~125 GeV. This is because of the conflict between the light gravitino mass
and heavy SUSY particle masses needed for producing the relatively heavy Higgs
boson mass. We consider two possible extensions in this paper: a singlet
extension of the Higgs sector, and strongly coupled gauge mediation. We show
that there is a large parameter space, in both scenarios, where the Higgs boson
mass of ~125 GeV is explained without any conflict with such a very light
gravitino.
