A keV-scale gravitino arsing from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that $Lambda$CDM model encounters in the modern cosmology could be alleviated with the keV-scale gravitino serving as the warm dark matter (WDM). Such a light gravitino asks for a low scale supersymmetry (SUSY) breaking for which the gauge mediation (GM) is required as a consistent SUSY-breaking mediation mechanism. In this paper, we show upperbounds of the masses of the second CP-even Higgs boson $H$ and the CP-odd Higgs boson $A$, assuming the keV-scale gravitino to be responsible for the current DM relic abundance: the upperbound on the mass of $H/A$ is found to be $sim 4$ TeV for the gravitino mass of $mathcal{O}(10$-$100)$ keV. Interestingly, the mass of $H/A$ can be as small as 2-3 TeV and the predicted $tanbeta$ is as large as 55-60 for the gravitino mass of $mathcal{O}(10)$ keV. This will be tested in the near future Large Hadron Collider (LHC) experiments.
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