Graphene-cellulose-polyethyleneimine aerogels (GA-MCC-PEI) were prepared using a simple, environmentally friendly method to remove anionic and cationic dyes in water. Graphene-cellulose hydrogels were prepared using a hydrothermal method and then immersed in a polyethyleneimine aqueous solution for 48 h to obtain graphene-cellulose-polyethyleneimine hydrogels, which were then freeze-dried. The light and porous composite aerogels had a good compression resistance, and the maximum allowable pressure of the graphene-cellulose-polyethyleneimine aerogel with a cellulose content of 43% was 21.76 kPa, which was 827 times its weight. Adsorption of the anionic dye amaranth and the cationic dye methylene blue by the graphene-cellulose-polyethyleneimine aerogel was satisfactorily modeled using the Langmuir isothermal equation, indicating monolayer adsorption. When the cellulose content was 39%, the equilibrium adsorption capacities of the composite aerogel for amaranth and methylene blue were 369.37 mg/g and 237.33 mg/g, respectively. This graphene-cellulose-polyethyleneimine aerogel can be used to remove dye pollutants in water to maintain ecological balance, thus broadening the application space of aerogel materials, that is, as adsorbents in different environments.