The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equation with nonlocal additional condition. It is shown that the nonlocal identification problem can be reduced to the initial-boundary value problem for nonlinear parabolic equation. Iteration method for numerical solution of this problem is proposed. Numerical results and their interpretation are presented for wide class of materials, including various values of valences and diffusivities of oxidized and reduced species.