Forbidden gaps of one-dimensional compound photonic crystals consisting of cholesteric liquid crystals sandwiched by periodic isotropic layers are investigated. The common forbidden gaps appear for both incident left and right polarization light which is different from the cholesteric liquid crystals. The forbidden gaps for incident left polarization light will disappear and the forbidden gaps for incident right polarization light will merge and become wider with the increasing of thickness ratio of cholesteric liquid crystals to periodic isotropic layers. The effect of forbidden gaps for incident left and right polarization light becomes obvious with the increasing of refractive index of periodic isotropic layers. The corresponding forbidden gaps for two colors of red, green and blue will appear by tuning thickness ratio of cholesteric liquid crystals to periodic isotropic layers and the refractive index of periodic isotropic layers, which can be used to fabricate reflective color filters for liquid display.