Seismic data acquired on land face multiple challenges due to the near-surface complexity. One of the challenges is the weathering layers’ influence due to the low velocity and rapidly varying nature of these layers. To overcome that, dense source-receiver sampling can be used to characterize the near-surface. However, that increases the acquisition costs, which makes it less attractive for large-scale seismic acquisition. An alternative approach is to use compressive sensing to acquire the data. Although it enables economical data acquisition, compressive sensing requires data reconstruction, which is another challenge in the presence of complex weathering layers. To overcome that, we propose a joint reconstruction and near-surface correction algorithm using a model-independent low-rank-based approach. We apply the method to synthetic and real data, which shows superior results compared with the conventional approach of near-surface correction followed by data reconstruction.