  We study a relic density of the flavino dark matter in modified Altarelli and
Feruglio $A_4$ model which is respecting the $SU(2)_L\times A_4\times Z_3\times
U(1)_R$ symmetry. We calculate the Lagrangian from the superpotential in the
model. In estimating relic density, we consider the relevant interactions from
the Lagrangian that realize the vacuum expectation value alignments and charged
lepton masses where we assume that the supersymmetry breaking effects are small
for flavon sector. As a result, we find the degenerate masses between the
lightest ``flavon'' and ``flavino'', and only two parameters in the potential
determines the relic density. Then allowed parameter space of these parameters
are estimated from relic density calculation taking a constraint from lepton
flavor violation into account. We also briefly discuss other dark matter
physics such as direct detection, indirect detection and collider search.
