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To realize efficient analysis of large scale planar periodic arrays, a two-level characteristic basis functions method accelerated with fast multipole method-fast Fourier transform (FMM-FFT) is developed in this paper. The characteristic basis functions (CBFs) for each element are constructed in a two-level framework, in which the CBFs construction based on plane wave derivation for single element at child level and the CBFs construction based on local interaction between array elements at father level are combined. The number of unknowns is reduced significantly by the two-level CBFs. Further, FMM-FFT is applied to expedite the computation of interaction between elements. Numerical results of large scale planar periodic arrays are given to demonstrate the validity and efficiency of the present method.