The lightning current waveform measurement module embedded in the surge protector provides data support for its aging analysis. To address the current issues in lightning current measurement within surge protectors, such as the inability to record complete waveforms and high noise levels, this study analyzes the characteristics of lightning current waveforms and designs a measurement circuit comprising a Rogowski coil, low-noise wideband amplification, single-ended to differential conversion, high-speed analog-to-digital converter, and FPGA. The processing of collected signals, caching and sending of data, and counting of lightning strikes are completed by FPGA. This design aims to reduce measurement errors in lightning current waveforms. A threshold and slope combining triggering method is employed to enhance the accuracy of counting lightning current impulses. Additionally, a method combining differential circuit and complete ensemble empirical mode decomposition with adaptive noise is proposed to reduce the influence of noise on lightning current waveform. Experimental tests were conducted using a lightning current composite wave generator from a lightning protection laboratory to evaluate the system and denoising methods. The results demonstrate that the system can accurately and comprehensively record lightning current waveforms. The lightning current measurement with the peak range of 1~10 kA has no leakage trigger phenomenon, a measurement error of ≤0.2 μs for half-peak arrival time, and a measurement error of ≤2.04% for the average slope of the front peak. The system will promote the intelligent development of surge protectors and provide data support for lightning research.