  The asymmetric dark matter (ADM) scenario can solve the coincidence problem
between the baryon and the dark matter (DM) abundance when the DM mass is of
${\cal O}(1)\,$GeV. In the ADM scenarios, composite dark matter is particularly
motivated, as it can naturally provide the DM mass in the ${\cal O}(1)\,$GeV
range and a large annihilation cross section simultaneously. In this paper, we
discuss the indirect detection constraints on the composite ADM model. The
portal operators connecting the $B-L$ asymmetries in the dark and the Standard
Model(SM) sectors are assumed to be generated in association with the seesaw
mechanism. In this model, composite dark matter inevitably obtains a tiny
Majorana mass which induces a pair-annihilation of ADM at late times. We show
that the model can be efficiently tested by the searches for the $\gamma$-ray
from the dwarf spheroidal galaxies and the interstellar electron/positron flux.
