A rigorous analysis of the scattering problem by the perfectly conducting strip loaded with a dielectric cylinder of different permittivity is presented. By introducing auxiliary electromagnetic fields and applying the reciprocity theorem, integral equations for the unknown electric field are derived. These integral equations are transformed into an equivalent matrix equation of infinite order with proper boundary conditions. By calculating inverse matrix of unknown coefficients from this equation, scattered electric fields are determined. In particular case of the dielectric with the same permittivity, the results of this paper correspond to well-known results.