The numerical schemes based on neural networks with a shifting aperture method to reconstruct a crack shape from eddy current test (ECT) signals are presented. Aiming at the final goal of ECT study and the reconstruction of the cracks that occur in the actual steam generator tubes of pressurized water reactor power plants, the cracks considered are not electrodischarge machined notches but the natural ones with distributed conductivity. The data are obtained from numerical simulations using an FEM-BEM coupling method based on the A-φ formulation. A database approach, a kind of fast forward solver, is also applied to save computational resources. The results obtained show that the inverse scheme proposed in this paper can give quite an accurate reconstruction and is robust against noises.