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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 inhomogeneouschiral condensate. Employing the Bloch's theorem, we show that all the modeshave opposite group velocity to the momentum in the low-momentum region and theenergy is minimized at non-zero momentum. Furthermore, the magnitude ofmomentum which realizes the minimum energy is equal to the wave number of thedensity wave.

Appearance of novel modes of $\bar{D}$ mesons in the Dual Chiral Density Wave