In this paper, the electromagnetic scattering problem related to a circular cylinder with inhomogeneous impedance boundary is solved. This kind of problem may have practical applications such as antenna design since one can obtain a certain radiation pattern by choosing the surface impedance in an appropriate way. The approach presented in this paper is based on the series representations of the scattering and incident fields. The impedance function is also expanded into a Fourier series. By using orthogonality properties of some special functions the problem is reduced to the solution of a system of linear equations. The problem is also solved through the extended boundary condition method (T-matrix method). Since an extensive treatment of the T-matrix method is available in the open literature the paper is weighted towards the Fourier series method. The results of both methods are compared. Some illustrative examples showing the effects of different parameters on the scattered field are given.