  We discuss the vacuum energy density and the cosmological constant of dS$_5$
brane world with a dilaton field. It is shown that a stable AdS$_4$ brane can
be constructed and gravity localization can be realized. An explicit relation
between the dS bulk cosmological constant and the brane cosmological constant
is obtained. The discrete mass spectrum of the massive scalar field in the
AdS$_4$ brane is used to acquire the relationship between the brane
cosmological constant and the vacuum energy density. The vacuum energy density
in the brane gotten by this method is in agreement with astronomical
observations.
