  We study gauge mediation models of supersymmetry breaking with neutralino
LSP. These models are naturally realized by embedding the usual
four-dimensional gauge mediation models into a higher-dimensional spacetime
such as $M^4 \times S^1 / Z_{2}$. We calculate the relic abundance of the
neutralino LSP in these models and show that there exist wide parameter regions
where the neutralino LSP constitutes the dominant component of the cold dark
matter. These regions evade constraints from collider experiments such as Higgs
mass bounds and $b \ra s \gamma$, and also provide the value for the muon
anomalous magnetic moment which is consistent with the SUSY explanation of the
deviation from the standard model prediction.
