We study a specific SUGRA model with nonuniversal gaugino masses as an
alternative to the minimal SUGRA model in the context of supersymmetric dark
matter. The lightest supersymmetric particle in this model comes out to be a
Higgsino dominated instead of a bino dominated lightest neutralino. The thermal
relic density of this Higgsino dark matter is somewhat lower than the
cosmologically favoured range, which means it may be only a subdominant
component of the cold dark matter. Nonetheless, it predicts favourable rates of
indirect detection, which can be seen in square-km size neutrino telescopes.Comment: Version to appear in Phys. Rev. D. A few references added in the
bibliography and a comment added in Section 2. LaTex, 16 pages, 4 figure