In this Letter, the spectral technique that has been applied to the finite-difference-time-domain (FDTD) method is applied to the alternating-direction-implicit higher-order FDTD (ADI-HO-FDTD) method for solving periodic structures, resulting in the periodic spectral (PS) ADI-HO-FDTD. The algorithm for inversion of the block periodic tri-diagonal matrices is presented. The effectiveness and computational efficiency of the proposed method are also shown. Numerical results indicate that the PS-ADI-HO-FDTD algorithm can save computation time by more than 27% in comparison with the conventional HO-FDTD method.