The present study investigates electromagnetic plane wave diffraction by a strip with two different surface impedances on both sides. On the strip, the Leontovich boundary conditions are satisfied on each surface. Then, the solution is obtained by the analytical-numerical method called orthogonal polynomials. The numerical results are analyzed with the fractional derivative method. The paper answers how to build up the mathematical background of the problem and provides near electric field distribution, and total radar cross-section for different cases.