A cholesteric liquid crystal (CLC) is a self-assembled photonic crystal formed by rodlike molecules, including chiral molecules, that arrange themselves in a helical fashion. The CLC has a single photonic bandgap and an associated one-colour reflection band for circularly polarized light with the same handedness as the CLC helix ( selective reflection)(1). These optical characteristics, particularly the circular polarization of the reflected light, are attractive for applications in reflective colour displays without using a backlight, for use as polarizers or colour filters(2-7) and for mirrorless lasing(8-12). Recently, we showed by numerical simulation that simultaneous multicolour reflection is possible by introducing fibonaccian phase defects(13). Here, we design and fabricate a CLC system consisting of thin isotropic films and of polymeric CLC films, and demonstrate experimentally simultaneous red, green and blue reflections ( multiple photonic bandgaps) using the single-pitched polymeric CLC films. The experimental reflection spectra are well simulated by calculations. The presented system can extend applications of CLCs to a wide-band region and could give rise to new photonic devices, in which white or multicolour light is manipulated.