An efficient algorithm for computing the scattering properties of multilayered periodic structures using a hybrid Finite-Difference Time-Domain/Generalized Scattering Matrix (FDTD/GSM) technique is described. In this technique, the constant-horizontal-wavenumber approach is used to compute the scattering parameters of each periodic layer. A complete Floquet harmonic analysis of the periodic structure is presented, where propagation and evanescent behaviors of Floquet harmonics are studied. In addition, guidelines for selection of higher-order harmonics for a certain layer separation are provided. The scattering matrix of each layer, including proper Floquet harmonics, is then cascaded together with those of the other layers to obtain the generalized scattering matrix of the entire structure. The validity of this algorithm was verified through several numerical examples, including frequency-selective surfaces (FSS) with different periodicities and under different incidence angles. The numerical results showed good agreement with the results obtained from the FDTD simulation of the entire structure, while the new procedure saved computational time and storage.