Using a network model, we investigate the localized modes of a 2-D photonic-crystal cavity. To this end, the propagation characteristics of the modes traveling along periodic cavities introduced in a bulk photonic crystal is determined. Using this method, the modal analysis of the periodic cavities can be reduced to the evaluation of natural frequencies of an equivalent network. It will be shown that by increasing the spacing of the successive cavities, the dispersion diagram of the periodic cavities tends to that of a single cavity. The calculated results are in good agreement with those reported in the literature using the plane-wave expansion method