  The thermal relic density of the neutralino dark matter in the brane world
cosmology is studied. Since the expansion law at a high energy regime in the
brane world cosmology is modified from the one in the standard cosmology, the
resultant relic density can be altered. It has been found that, if the five
dimensional Planck mass $M_5$ is lower than $10^4$ TeV, the brane world
cosmological effect is significant at the decoupling time and the resultant
relic density is enhanced. We calculate the neutralino relic density in the
Constrained Minimal Supersymmetric Standard Model (CMSSM) and show that the
allowed region is dramatically modified from the one in the standard cosmology
and eventually disappears as $M_5$ is decreasing. We also find a new lower
bound on $M_5 \gtrsim 600$ TeV based on the neutralino dark matter hypothesis,
namely the lower bound in order for the allowed region of the neutralino dark
matter to exist.
