Pharmaceutical products such as antibiotics, analgesics, steroids, and non-steroidal anti-inflammatory drugs (NSAIDs) are new emerging pollutants, often present in wastewater, potentially able to contaminate drinking water resources. Adsorption is considered the cheapest and most effective technique for the removal of pollutants from water, and, recently, membranes obtained by wet filtration method of SWCNT aqueous solutions (SWCNT buckypapers, SWCNT BPs) have been proposed as self-standing porous adsorbents. In this paper, the ability of graphene oxide/single-walled carbon nanotube composite membranes (GO-SWCNT BPs) to remove some important NSAIDs, namely Diclofenac, Ketoprofen, and Naproxen, was investigated at different pH conditions (pH 4, 6, and 8), graphene oxide amount (0, 20, 40, 60, and 75 wt.%), and initial NSAIDs concentration (1, 10, and 50 ppm). For the same experimental conditions, the adsorption capacities were found to strongly depend on the graphene oxide content. The best results were obtained for 75 wt.% graphene oxide with an adsorption capacity of 118 ± 2 mg g−1 for Diclofenac, 116 ± 2 mg g−1 for Ketoprofen, and 126 ± 3 mg g−1 for Naproxen at pH 4. Overall, the reported data suggest that GO-SWCNT BPs can represent a promising tool for a cheap and fast removal of NSAIDs from drinking water resources, with easy recovery and reusability features.