Induced polarization (IP) tomography measurements as a near-surface geophysical method can provide information about the degree of chargeability of subsurface materials, and are commonly used in mineral exploration, engineering studies (e.g., sediment/bedrock interface identification, crushed zones and faults detection, and landslide and soil properties imaging.), as well as in environmental investigations (contaminant plums identification and landfill characterization). The purpose of these measurements is to obtain the distribution of polarizability characteristics inside an object, generally below the surface, at the boundary of the object, or outside the area in question. The result of such measurements can be mathematically modeled for the specific polarizability properties by the solution of Poisson’s equation restricted by appropriate boundary conditions. In this paper, we focus on the importance of simulating induced-polarization responses and retrieving chargeability distributions in geo-materials to enhance the characterization of subsurface structures. We present the methods for forward modeling and nonlinear inversion of induced-polarization measurements. To this end, in the first step, Poisson’s equation for a two-dimensional ground with arbitrary distribution of conductivity is solved using the finite difference numerical method and in the next step, based on the existing relations between conductivity and chargeability (Siegel’s formulation), the apparent induced polarization response is calculated. Finally, we solve the nonlinear chargeability inversion problem following a nonlinear apparent resistivity inversion. This is achieved by imposing physical constraints to prevent the estimation of unrealistic model parameters, using a Newton-based optimization method. To evaluate the efficiency of the proposed methodology, we utilized the proposed algorithm to two simulated examples and a real data set. Our numerical results show that the algorithm reliably represents the main features and structure of the Earth’s subsurface in terms of the resistivity and chargeability models. All the algorithms presented in this paper have written in the MATLAB programming language.