A method to reconstruct the inhomogeneous surface impedance of a cylindrical body through the measured far-field scattering data is given. The scattered field is represented as a single-layer potential which leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. The use of the jump relations for the single-layer potential enables the evaluation of the total field and its derivative on the boundary of the scatterer. Then, the surface impedance is reconstructed from the boundary condition itself either by direct evaluation or by a minimum norm solution in the least-squares sense. The numerical results show that the method yields good resolution.