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The electromagnetic wave propagation in the chiral medium is goved by Maxwell’s equations together with the Drude-B-Fedorov (constitutive) equations.The problem is simplified to a two-dimensional scattering problem,and is formulated in a bounded domain by introducing two pairs of transparent boundary conditions.An a posteriori error estimate associated with the truncation of the nonlocal boundary operators is established.Based on the a posteriori error control,a finite element adaptive strategy is presented for computing the diffraction problem.The truncation parameter is determined through sharp a posteriori error estimate.Numerical experiments are included to illustrate the robustness and effectiveness of our error estimate and the proposed adaptive algorithm.