By combining the advantages of poly(4-styrenesulfonic acid-co-maleic acid) sodium (PSSMA) with abundant anionic functional groups (–COO⁻ and –SO₃⁻), graphene oxide (GO) with high specific surface area and Fe₃O₄ nanoparticles with excellent magnetic responsiveness, a novel type of PSSMA-modified magnetic reduced graphene oxide nanocomposite (PSSMA/M-rGO) was synthesized via a simple and facile one-step solvothermal method and used for removing cationic dyes from aqueous solutions in this study. The as-synthesized PSSMA/M-rGO was characterized by Fourier transform infrared spectroscopy, UV-vis spectroscopy, scanning electron microscopy, transmission electron microscopy, thermogravimetric analysis, X-ray diffraction, vibrating sample magnetometry, dynamic light scattering and nitrogen adsorption-desorption technique. Three typical cationic dyes, basic fuchsin (BF), crystal violet (CV) and methylene blue (MB) were used as model dye pollutants to evaluate the adsorption performance of the resultant PSSMA/M-rGO. The adsorption of three cationic dyes onto both PSSMA/M-rGO and M-rGO without PSSMA modification on the surface were systematically investigated at different experiment conditions. The results indicate that the binding of PSSMA on M-rGO can significantly enhance the adsorption capacities and removal efficiencies of the three dyes. This is due to the rich –COO⁻ and –SO₃⁻ groups on PSSMA/M-rGO having strong electrostatic interactions with the positively charged dye molecules. The adsorption kinetics and isotherms of the three dyes onto both adsorbents demonstrate that the kinetics and equilibrium adsorptions can be well-described by pseudo-second-order kinetics and Langmuir model, respectively. Moreover, the PSSMA/M-rGO nanocomposites also demonstrate high removal efficiencies toward mixed dyes of BF, CV and MB. Such functional nanocomposites with high adsorption capacity, low production cost and excellent recyclability, are promising as candidate adsorbents for highly-efficient removal of cationic organic pollutants from aqueous solutions.