We consider the mass spectroscopy of dark matter in the dark hadron model. In the dynamical chiral symmetry breaking in the $SU(3)$ hidden color gauge sector, there exist Nambu-Goldstone bosons which are massive because the hidden sector fermions break explicitly chiral symmetry. Therefore, these bosons are dark matter candidates. We study $SU(3)$ hidden color interaction and $SU(3)$ hidden flavor symmetry, which can be broken into $SU(2)_V \times U(1)$. We present the mass spectroscopy of dark matter by lattice QCD simulations with Wilson fermions and truncated overlap fermions based on domain wall fermions. Truncated overlap fermions satisfy lattice chiral symmetry instead of the chiral symmetry in continuum field theory.