This paper describes an efficient nondestructive evaluation (NDE) eddy-current (EC) system using an improved giant magnetoresistance magnetometer (IGMRM) and a simple single wire as inducer. A three-dimensional finite-element method (3-D FEM) was implemented to evaluate the theoretical expected response of the system. The model was based on a modified magnetic vector potential and a reduced magnetic scalar potential, in conducting and nonconducting regions, respectively. The model robustness is established by comparing numerical and experimental results on a given benchmark aluminum plate sample. This efficient 3-D FEM model helps to understand the system performances. Moreover, the excitation frequency effect on the sensed signal is analyzed versus the benchmark sample thickness and the crack sizes. Results are also given and discussed in terms of signal-to-noise ratio.