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.