In stepped-frequency continuous-wave ground-penetrating radar (SFCW GPR) systems, complex noises such as coupling noise, ground harmonic noise, and external electromagnetic interference significantly degrade the signal quality, thus severely affecting the accuracy of target detection. Although conventional denoising methods such as wavelet transform, mean clustering, and fuzzy mean clustering perform well in pulsed radar systems, they exhibit inherent limitations in suppressing time-domain cumulative noise in continuous-wave radar signals. To address this issue, this study proposes a novel noise-suppression method for SFCW GPR based on the variational mode decomposition algorithm. This method decomposes a noisy signal into several intrinsic mode functions and reconstructs an effective signal based on center-frequency-based screening of the modal functions, thereby significantly enhancing the denoising performance. Simulation experiments demonstrate that the proposed method improves the signal-to-noise ratio by approximately 13.16 dB. Practical experiments further confirm the effectiveness of the method in noise suppression, where the power spectral densities of both high- and low-frequency noise in the processed signal are approximately 0 W/Hz. This study provides a reliable solution for the application of ground-penetrating radar in complex noise environments.