  By extending a previously proposed conformal gauge mediation model, we
construct a gauge-mediated SUSY breaking (GMSB) model where a SUSY-breaking
scale, a messenger mass, the $\mu$-parameter and the gravitino mass in a
minimal supersymmetric (SUSY) Standard Model (MSSM) are all explained by a
single mass scale, a R-symmetry breaking scale. We focus on a low scale
SUSY-breaking scenario with the gravitino mass $m_{3/2}=\mathcal{O}(1){\rm
eV}$, which is free from the cosmological gravitino problem and relaxes the
fine-tuning of the cosmological constant. Both the messenger and SUSY-breaking
sectors are subject to a hidden strong dynamics with the conformality above the
messenger mass threshold (and hence the name of the model "strongly interacting
conformal gauge mediation"). In our model, the Higgs B-term is suppressed and a
large $\tan\beta$ is predicted, resulting in the relatively light second
CP-even Higgs and the CP-odd Higgs with a sizable production cross section.
These Higgs bosons can be tested at future LHC experiments.
