Eddy current testing (ECT) usually employs a sinusoidal current that flows through an excitation coil. If a square wave instead of a sinusoidal wave is used for excitation, i.e., a square-wave inverter instead of linear amplifiers is used for an ECT system, a handheld ECT system can be developed and the cost can be reduced. In this study, we developed a low-frequency ECT (LF-ECT) system with a square-wave inverter to determine whether an inverter is applicable to estimating the thickness of a thick steel plate in the range from 6 to 19 mm. The developed ECT system has a differential excitation coil and a pickup coil, and these coils are arranged on the steel plate. A square-wave voltage is applied to the excitation coil, and the voltage of the pickup coil is measured. Subsequently, the mutual equivalent resistance and inductance are calculated. Results indicate that the fundamental component of the resistance increases with the thickness when the frequency is approximately 4 Hz. Furthermore, we determined whether the harmonic signals generated by the inverter are also useful. Results indicate that the harmonic components of the resistance also tend to increase with a sufficiently small increase in thickness, i.e., ≤12 mm. This implies that surface and back-surface defects can be simultaneously obtained.