We report that polarization modulation reflectance (PMR) spectroscopy is highly sensitive to the cavity polaritons in a ZnO microcavity with HfO2/SiO2 distributed Bragg reflectors. We demonstrate that the cavity-polariton dispersion, even in the energy region of strong absorption by exciton continuum states, is clearly observed by PMR spectroscopy. The PMR spectra were quantitatively analyzed by a transfer-matrix method taking into account three types of excitons labeled A, B, and C. Line-shape analysis of the PMR spectra indicates that the anisotropy of the excitonic transitions is considerable in treating the cavity polariton in the ZnO microcavity.