  We investigate the thermal relic density of a cold dark matter in the brane
world cosmology. Since the expansion law in a high energy regime is modified
from the one in the standard cosmology, if the dark matter decouples in such a
high energy regime its relic number density is affected by this modified
expansion law. We derive analytic formulas for the number density of the dark
matter. It is found that the resultant relic density is characterized by the
``transition temperature'' at which the modified expansion law in the brane
world cosmology is connecting with the standard one, and can be considerably
enhanced compared to that in the standard cosmology, if the transition
temperature is low enough. The implication to the neutralino dark matter also
is mentioned.
