In this study, the preparation of a new, functional anion-exchange membrane (AEM), containing guanidinium groups as the anion-exchanging sites (Gu-100), is described as well as the membrane characterization by XPS, water uptake, permselectivities, and electrical resistances. The functional membrane was also employed in pH-dependent electrodialysis experiments using model dairy wastewater streams. The properties of the new membrane are compared to those of a commercially available anion-exchange membrane bearing conventional quaternary ammonium groups (Gu-0). Guanidinium was chosen for its specific binding properties toward oxyanions: e.g., phosphate. This functional moiety was covalently coupled to an acrylate monomer via a facile two-step synthesis to yield bulk-modified membranes upon polymerization. Significant differences were observed in the electrodialysis experiments for Gu-0 and Gu-100 at pH 7, showing an enhanced phosphate and citrate transport for Gu-100 in comparison to Gu-0. At pH 10 the difference is much more pronounced: for Gu-0 membranes almost no phosphate and citrate transport could be detected, while the Gu-100 membranes transported both ions significantly. We conclude that having guanidinium groups as anion-exchange sites improves the selectivity of AEMs. As the presented monomer synthesis strategy is modular, we consider the implementation of functional groups into a polymer-based membrane via the synthesis of tailor-made monomers as an important step toward selective ion transport, which is relevant for various fields, including water treatment processes and fuel cells.