Water pollution caused by highly toxic arsenic (As) and lead (Pb) poses a serious threat to water quality. Hence, the development of materials for their effective removal from water continues to attract research attention. The present study reports functionalized graphitic carbon nitride nanosheets (GCN) as a green and low-cost adsorbent for the removal of As and Pb from polluted water. The adsorbent was prepared through the protonation and hydroxyl and cyano functionalized graphitic carbon nitride to form H/GCN and OH/CN-GCN respectively. Characterization techniques including Fourier transform infrared (FTIR), X-ray diffraction, and scanning electron microscopy were respectively used to study functional groups, structure, and morphology of the adsorbents. The adsorption study showed that modification of GCN with −OH and CN− ions in OH/CN-GCN, increased the density of negative charges on the functionalized surface, which also enhances the attraction of the positively charged ions. This may be responsible for the improved removal of As and Pb from wastewater compared to H/GCN. Isotherm studies on the adsorption behavior of OH/CN-GCN suggest that Langmuir isotherm model corroborates with the As adsorption. Therefore, indicating that the removal of As via its adsorption onto OH/CN-GCN is a surface phenomenon. However, the adsorption of Pb could be described as mainly a multilayer adsorption process, based on its R2 value. It is proposed that the −OH and CN− groups on the tri-s-triazine units of GCN nanosheets may be responsible for the adsorption process. The prepared materials are promising adsorbents that nay find useful applications in wastewater treatment plants involving advanced oxidation processes.