Pulsed eddy current has attracted increasing attention to ferromagnetic metal material evaluation since it possesses low power consumption and abundant frequency spectrum advantages. However, when a current source is applied to generate the pulse excitation signal in eddy current testing, the inductance of driver coil induces a large reverse electromotive force in the excitation circuit, which distorts the pulse excitation signal as the excitation circuit hardly satisfies the severe power and stability requirements for counteracting the reverse induced electromotive force. Therefore, a pulsed eddy current field excited by a voltage-driven coil placed concentrically to a ferromagnetic casing is studied, and the analytic solutions of it are formulated in this paper. In contrast to current source based pulsed eddy current testing methods, the electromotive force induced by the coil’s inductance and eddy current is analyzed. Furthermore, a new pulse excitation function is adopted and induced electromotive force equations of pick-up coils are formulated based on the superposition principle of magnetic field. Finally, the theoretical results are verified by experiments.