In this paper the problem of microwave imaging of an impedance cylinder is investigated with Newton's method. To this aim, the scattered field from a circular cylinder with homogeneous impedance is derived for plane wave illumination. In this step, the scattering configuration is assumed as a TMz scenario, where the impedance cylinder is infinite in z axis and the electric fields are parallel to the same axis. Then, in the inverse scattering phase the impedance and the radius of the target have to be estimated. To this purpose, an initial value is assigned to both variables and the scattered field corresponding to these initial values is evaluated. The difference between the scattered fields is divided to a matrix, which contains the derivative of the scattered field with respect to unknown variables, to estimate the update amount for each parameter. Then, both parameters are updated and this process continues up until to the difference between the measured and the calculated fields goes below to a predefined threshold. Thus, an estimate of the impedance and the radius of the cylinder is obtained. Results show that the proposed method can reconstruct the unknown parameters with limited aperture - multiple frequency measurements.