  We calculate dispersion relations for $\bar{D}(0^-)$, $\bar{D}^*(1^-)$,
$\bar{D}_0^*(0^+)$ and $\bar{D}_1(1^+)$ mesons in the Dual Chiral Density Wave
(DCDW) where the chiral symmetry is spontaneously broken by inhomogeneous
chiral condensate. Employing the Bloch's theorem, we show that all the modes
have opposite group velocity to the momentum in the low-momentum region and the
energy is minimized at non-zero momentum. Furthermore, the magnitude of
momentum which realizes the minimum energy is equal to the wave number of the
density wave.
