Migration noise exists in the frequency-wavenumber migrated profile of ground-penetrating radars (GPRs) in tunnel linings. To address these artifacts and enhance the resolution and accuracy of the actual GPR-detection section, a total variation (TV)-regularization algorithm is constructed based on split Bregman iteration. First, the objective function of TV regularization is formulated based on the noisy migration section. Thereafter, the regularization term is approximated by the Bregman distance, enabling the decoupling of the regularization and data non-fitting terms. This transforms the objective-function solution into an optimization problem. Finally, the Gauss-Seidel iterative calculation is employed to solve the resulting problem. The noise suppression of the migration profile is realized by leveraging the minimization characteristic of the TV norm. The efficacy and practicability of the proposed method are validated using a tunnel-lining steel-structure model and field-measured GPR data from an operational tunnel lining. The results reveal the following: (1) the proposed algorithm effectively suppresses diffraction arcs and artifacts caused by high-frequency interferences while preserving the boundary information in the GPR image; (2) the denoising performance of the algorithm is primarily governed by the regularization parameters and the convergence threshold, which can be optimized based on the calculation efficacy and cost in real data processing; and (3) the algorithm effectively suppresses the migration artifacts and residual noise, enhances the signal-to-noise ratio and spatial accuracy of the GPR profile, and demonstrates good adaptability to real data.