The high-performance electromagnetic wave (EMW) absorption materials have great potential in both civil and military fields. A novel approach to prepare the reduced graphene oxide covalently grafted polyaniline (rGO-g-PANI) nanocomposites with the strong absorption intensity and broad bandwidth was employed in this paper. Specifically, the aniline monomers were bonded with the graphene oxide (GO) nanosheets via the nucleophilic ring-opening reaction of epoxy groups of GO. Coupling with the role of the reducer, rGO modified with aniline (rGO-An) was prepared. Subsequently, the rGO-g-PANI nanocomposites were synthesized by the interfacial polymerization, in which the rGO-An nanosheets served as the reactivity point for the interfacial polymerization of aniline, and PANI nanorods grew vertically on the rGO nanosheets. The calculated results of electromagnetic parameters suggest that the minimum reflection loss of the rGO-g-PANI nanocomposites can reach up to -60.3dB at the frequency of 11.1GHz with the thickness of 2.86mm, and the effective absorption bandwidth less than -10dB (90% microwave absorption) is as wide as 4.7GHz (from 9.3 to 14GHz) when the content of rGO-g-PANI in the paraffin matrix is 30wt%. Compared with the rGO/PANI nanocomposites prepared via non-covalent absorption, the microwave absorption performance of the rGO-g-PANI nanocomposites has been greatly enhanced. The results in turn demonstrate that the covalent bonds between rGO nanosheets and PANI nanorods can facilitate the formation of the highly conductive networks, further promoting the EMW absorption.