Natural gas sweetening currently requires multistep, complex separation processes to remove the acid gas contaminants, carbon dioxide and hydrogen sulfide. In addition to being widely recognized as energy inefficient and cost-intensive, the effectiveness of this conventional process also suffers considerably because of limitations of the sorbent materials it employs. Herein, we report a new porous organic polymer, termed KFUPM-5, that is demonstrated to be effective in the concurrent separation of both hydrogen sulfide and carbon dioxide from a mixed gas stream at ambient conditions. To understand the ability of KFUPM-5 to selectively capture these gas molecules, we performed both pure-component thermodynamic and mixed gas kinetic adsorption studies and correlated these results with theoretical molecular simulations. Our results show that the underlying polar backbone of KFUPM-5 provides favorable adsorption sites for the selective capture of these gas molecules. The outcome of this work lends credence to the prospect that, for the first time, porous organic polymers can serve as sorbents for industrial natural gas sweetening processes.