This paper presents the operation principle and design rule of the Rogowski coil which can measure the transient current and describes the calibration and application experimental results for performance evaluation. It is obtained that the response curves of the Robowski coil with the turns of 300 and the passive integrator to sinusoidal input give a good linearity up to the frequency of 500 [kHz] and the current measurement system gaving the Rogowski coil is the frequency bandwidth of 40 [Hz]~700 [kHz]. As an application experiment for the fabricated modeling power transmission line, the impulse current, which limitates the direct lightning return stroke to overhead ground wire, is measured by the Rogowski coil and its fast Fourier transformation is carried out. The equivalent circuit of the Rogowski coil considering the stray capacitances is proposed, and the theoretical analysis is in good agreement with the measurement results. Also, it is found that for high frequency domain the stray capacitance such as a distributed capacitance to the shield and the capacitance between windings of coil should be considered in designing the Rogowski coils since the resonance originates from the stray capacitance and the self-inductance of the Rogowski coil.