Low-scale gauge-mediated supersymmetry(SUSY)-breaking (GMSB) models with gravitino mass m(3/2) < 16 eV are attractive, since there are no flavor and cosmological problems. In this paper, we thoroughly study the collider signal in the case that the next-to-lightest SUSY particle is the bino or slepton and investigate the discovery potential of the LHC. Our result is applicable to a wider class of GMSB models other than the minimal GMSB models and we pay particular attention to realistic experimental setups. We also apply our analysis to the minimal GMSB models with a metastable SUSY-breaking vacuum and we show, by requiring sufficient stability of the SUSY-breaking vacuum, these models can be tested at an early stage of the LHC.