The interactions of sodium diclofenac drug (s-DCF) with different graphene species were investigated using both first principles calculations based on Density Functional Theory (DFT) and adsorption experiments. Through batch adsorption experiments, it was found that rGO was a good adsorbent for removing the s-DCF drug from aqueous solutions. The general-order kinetic model shows the best fit to the experimental data compared with pseudo-first order and pseudo-second order kinetic adsorption models. The equilibrium data (at 25 °C) were fitted to the Liu isotherm model. The maximum sorption capacity for adsorption of the s-DCF drug was 59.67 mg g(-1) for rGO. The s-DCF adsorption onto pristine graphene, graphene with a vacancy, reduced oxide graphene (rGO) and functionalized graphene nanoribbons were simulated providing a good understanding of the adsorption process of this molecule on graphene-family surfaces. The results predict a physisorption regime in all cases. Based on these results, the ab initio calculations and the adsorption experiments point out that the graphene-family are promising materials for extracting s-DCF from wastewater effluents.