In this talk, we mainly focus on the mathematical analysis and numerical calculation for an inverse scattering of an impedance obstacle embedded in a complex medium. The scattering problem can be modeled as a second-order elliptic system with proper boundary conditions. The unique solvability of the direct scattering problem and the complex analyticity of its solution are proved. We are concerned with a corresponding inverse scattering problem, and prove that the cylinder can be uniquely determined from the far-field measurements. Finally, we will introduce our ongoing research work.