A method to reconstruct the one-dimensional profile of a cylindrical layer with an inhomogeneous impedance boundary is proposed. Through the finite Fourier transformation of the field expressions the problem is first reduced to the solutions of a two-coupled system of operator equations which is solved iteratively starting from an initial estimate of the profile. The reconstruction of the profile is achieved by linearizing one of the equations in the Newton sense. The method is tested by considering several numerical examples and yields satisfactory reconstructions. As is typical for Newton-type methods, the convergence of the iteration depends on the initial guess.