Two inversion methods for electromagnetic scattering, the deterministic gradient search method and the Monte Carlo random search method， are proposed in this paper. Firstly, the fundamental principles of the two methods are introduced. Inversion properties including the positioning capability of the scattering body, inversion accuracy and inversion time of the two methods are analyzed and compared. Simulation results demonstrates that the deterministic gradient search method can be used for scattering body positioning and the results using Monte Carlo random search method have high-precision at the same time have high speed. Successive applications of both methods fully realize the advantages of the two methods and improve the inversion result.