High-performance electromagnetic absorption (EMA) based on conductive coordination polymers seems interesting but still remains unexplored to date. Herein, we systematically investigated the EMA properties of Cu(I)–thiophenolates with low dimensional nanostructures. The results indicate a structure-correlated EMA performance of the Cu(I)–thiophenolates, where the two-dimensional nanosheets an exhibit excellent broadband EMA, while the one-dimensional nanorods shows very low EMA. A well-constructed conductive Cu–S network with the combination of dielectric loss and magnetic loss is thought to be the main reason for the high-performance EMA of the two-dimensional Cu(I)–thiophenolates. It opens up the exploration and development of conductive metal–organic complexes in the area of EMA.