To address the accommodation-convergence conflict problem in conventional augmented reality (AR) head-mounted displays, we propose a compact multi-plane display design based on cholesteric liquid crystal (CLC) reflective films and a polarization switch. Because of the polarization selectivity of CLC films, circularly-polarized light with different handedness is reflected by different CLC films, resulting in different optical path lengths and different image depths by the lens. A flicker-free dual-plane prototype with correct focus cues and relatively low operating voltage has been implemented. Moreover, a multi-plane AR display scheme with more than 2 depth planes is proposed by stacking multiple CLC films and polarization switches together.