  We study the diphoton signal of the Higgs boson in gauge mediated
supersymmetry breaking models, which can explain both the Higgs boson mass of
around 125 GeV and the result of the muon g-2 experiment. We consider two
possible extensions of gauge mediation models: inclusion of vector-like
matters, and a mixing between a messenger and the up-type Higgs. The large
left-right mixing of staus is induced in both scenarios, resulting in the
enhanced diphoton signal. We include a constraint from a charge breaking
minimum, which is severe for the large left-right mixing of staus. The
branching fraction of h to gamma gamma can be about 40 percent larger than that
of the Standard Model Higgs boson, in the region of parameter space where the
Higgs boson mass of around 125 GeV and the muon g-2 are explained.
