As the world develops technologically and economically, the issue of environmental pollution has garnered increasing attention. Cellulose, the most abundant natural polymer on Earth, offers a promising solution. Cellulose-based aerogels are cost-effective, environmentally friendly, and effective at absorbing oil and organic pollutants. However, their absorption capacity is still limited. It requires the new method to modify the structure of cellulose aerogel and address this problem. In this work, by chelating silver ions with melamine and cellulose nanofibers through freeze-drying, the melamine–cellulose nanocomposite (Ag⁺-MNC) aerogels are prepared, which are tested for their ability to absorb various oils and organic solvents. The effects of nanocellulose and Ag⁺ concentrations on the absorption performance of nanocomposite aerogel are evaluated. The results show that the Ag⁺-MNC aerogels possess the very high absorption capacities with the values of 157.58 ± 3.38, 199.47 ± 5.65, 120.96 ± 7.04, 239.40 ± 7.41, 142.83 ± 5.30, 103.30 ± 4.73, 124.03 ± 4.05, and 118.95 ± 6.53 g/g for acetone, ethyl acetate, cyclohexane, dichloromethane, ethanol, kerosene, pump oil, and waste pump oil, respectively, which are 419%, 584%, 248%, 175%, 505%, 180%, 293%, and 268% higher than pure nanocellulose aerogels. Our Ag⁺-MNC aerogel has potential application in the absorption of oils and organic solvents.