  We consider a recently proposed supersymmetric radiative seesaw model which
is coupled with the minimal supergravity. The conventional R parity and $Z_2$
invariance are imposed, which ensures the existence of a multi-component dark
matter system. We assume that the pair of the lightest neutralino
$\tilde{\chi}$ and the fermionic component $\tilde{\xi}$ of the inert Higgs
supermultiplet is dark matter. If $\tilde{\xi}$ is lighter than $\tilde{\chi}$,
and the lightest neutral inert Higgs boson is kinematically forbidden to decay
(third dark matter), the allowed region in the $m_0{\rm \mathchar`-}M_{1/2}$
plane increases considerably, where $m_0$ and $M_{1/2}$ are the universal
soft-supersymmetry-breaking scalar and gaugino mass, respectively, although the
dominant component of the multi-component dark matter system is $\tilde{\chi}$.
There is a wide allowed region above the recent LHC limit.
