We have investigated optical characteristics of a one-dimensional dual photonic crystal with helix. We have confirmed the particular defect mode at the band edges of CLC has high Q-factor. The defect mode with high Q-factor existed at ally conditions regardless of the polarization of incident light, helical pitch and thickness of the CLC. All defect modes in the photonic band gap could be divided in two groups. The first one was the defect modes whose Q-factor became high at the long-wavelength edge of the CLC band. The other one was that at the short-wavelength edge of the CLC.