Ground penetrating radar (GPR) is susceptible to clutter interference, such as coupling waves and direct ground-surface waves, in road disease detection. Existing low-rank and sparse clutter suppression methods using L1-norm regularization can characterize point-like targets like cavities but struggle to preserve the continuous structural features of volumetric diseases such as voids and loose areas. To address this, this paper proposes a GPR clutter suppression method based on weighted nuclear norm minimization and structured sparsity constraints. The method utilizes a weighted nuclear norm to model the low-rank property of clutter, where weights that adaptively vary with singular values impose stronger shrinkage on large singular values corresponding to strong clutter while preserving small singular values corresponding to weak target components. Meanwhile, in the sparse term, the L1-norm and group sparse regularization are jointly incorporated to characterize point-like sparse targets and structural targets, respectively. For the solution strategy, the fast alternating direction method of multipliers (ADMM) is employed to iteratively solve the low-rank and sparse decomposition model, achieving efficient separation of the low-rank background and structured targets, and truncated singular value decomposition (SVD) is used in place of full SVD to reduce computational complexity. Experiments on both simulated and measured data demonstrate that the proposed method achieves significant performance improvements in road cavity and loose area scenarios. On simulated data, the peak signal-to-noise ratio (PSNR) is improved by more than 3 dB on average compared with methods such as mean suBtraction (MS), principal component analysis (PCA), singular value decomposition (SVD), and robust nonnegative matrix factorization(RNMF), and the structural similarity (SSIM) reaches up to 0.971 8. On measured GPR data, the signal-to-clutter ratio (SCR) increases to 9.49 and the improvement factor (IF) reaches 32.87, significantly outperforming the compared algorithms. The results show that the proposed method can effectively suppress strong clutter, enhance the response of structural disease targets, and exhibit good robustness and engineering applicability.