An eddy current nondestructive testing using the Surface Impedance Boundary Condition (SIBC) and Efficient Global Optimization (EGO) is proposed in this paper. We solve the forward problem of a conducting tube comprising a defect, with a finite element method using femm package software. We use the SIBC condition to represent the tube with defect and we compute the impedance variations of the probe. This variation is used as an input for the inverse problem. Next, the EGO algorithm is used for defect characterization. The main goal of this work is to improve computation time when evaluating cost functions in inversion algorithms. Simulation results show the efficiency of the proposed fit in terms of computation time and accuracy of estimating geometric parameters.