A series of carbon nanotubes doped with Fe and/or Cu, Fe100−xCux/CNT (x = 0, 25, 50, 75 and 100) has been prepared by an easy method of wetness impregnation of commercial multiwalled carbon nanotubes previously oxidized with nitric acid. The wide characterization of the solids by different techniques demonstrates that the incorporation of Fe and Cu to the CNTs has been successfully produced. Fe100−xCux/CNT samples were tested as catalysts in the removal of paracetamol from aqueous solution by a combined process of adsorption and Fenton-like oxidation. Under mild conditions, 25 °C and natural pH of solution, i.e., nearly neutral, values of oxidation of paracetamol between 90.2% and 98.3% were achieved after 5 h of reaction in most of cases. Furthermore, with the samples containing higher amounts of copper, i.e., Cu100/CNT and Fe25Cu75/CNT, only 2 h were necessary to produce depletion values of 73.2% and 87.8%, respectively. The influence of pH and dosage of H2O2 on the performance has also been studied. A synergic effect between both Cu+/Cu2+ and Fe2+/Fe3+ in Fenton-like reaction was observed. These results demonstrate that Fe100−xCux/CNT are powerful Fenton-like catalyst for degradation of paracetamol from aqueous solution and they could be extended to the removal of other organic pollutants.