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A periodic finite-difference time-domain (FDTD) analysis is presented and applied for the first time in the study of a two-dimensional (2D) leaky-wave planar antenna based on dipole frequency selective surfaces (FSSs). First, the effect of certain aspects of the FDTD modeling in the modal analysis of complex waves is studied in detail. Then, the FDTD model is used for the dispersion analysis of the antenna of interest. The calculated values of the leaky-wave attenuation constants suggest that, for an antenna of this type and moderate length, a significant amount of power reaches the edges of the antenna, and thus diffraction can play an important role. To test the validity of our dispersion analysis, measured radiation patterns of a fabricated prototype are presented and compared with those predicted by a leaky-wave approach based on the periodic FDTD results.