  The thermal relic density of the wino-like neutralino dark matter in the
brane world cosmology is studied. The expansion law at a high energy regime in
the brane world cosmology is modified from the one in the standard cosmology,
and the resultant relic density can be enhanced if the five dimensional Planck
mass $M_5$ is low enough. We calculate the wino-like neutralino relic density
in the anomaly mediated supersymmetry breaking scenario and show that the
allowed region is dramatically modified from the one in the standard cosmology
and the wino-like neutralino with mass of order 100 GeV can be a good candidate
for the dark matter. Since the allowed region disappears eventually as $M_5$ is
decreasing, we can find a lower bound on $M_5 \gtrsim 100$ TeV according to the
neutralino dark matter hypothesis, namely the lower bound in order for the
allowed region of the neutralino dark matter to exist.
