Now electromagnetic nondestructive testing methods have been applied to many fields of engineering. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, scale, and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell′s equations (2D and 3D). A perturbation homotopy method combined with damping Gauss‐Newton methods is applied to the inverse electromagnetic problem. This method differs from traditional homotopy method. The structure of homotopy function is similar to Tikhonov functional. Sets of solutions are produced by perturbation for every homotopy parameter λ = λi, i = 0, …, L. At each iterative step of the algorithm, we add stochastic perturbation to numerical solutions. The previous solution and perturbation solution are regarded as the initial value in the next iteration. Although the number of solution in set increased, it increased the likelihood of obtaining correct solution. Results exhibits clear advantages over damping Gauss‐Newton method and testify that it is an available method, especially on aspects of wide convergence and precision.