Purpose -- The purpose of this paper is to provide a new methodology for the characterization of a defect by eddy-current testing ({ECT}). The defect is embedded in a conductive non-magnetic plate and the measured data are the impedance variation of an air-cored probe coil scanning above the top of the plate. Design/methodology/approach -- The inverse problem of defect characterization is solved by an iterative global optimization process. The strategy of the iterations is the kriging-based expected improvement ({EI}) global optimization algorithm. The forward problem is solved numerically, using a volume integral approach. Findings -- The proposed method seems to be efficient in the light of the presented numerical results. Further investigation and comparison to other methods are still needed. Originality/value -- This is believed to be the first time when the EI algorithm has been used to solve an inverse problem related to the {ECT}.