New high percolating alginate membranes are designed without using sophisticated drying methods: negatively charged alginate reacts with positively charged polyethylenimine (PEI), prior to be crosslinked with glutaraldehyde and air-dried. This is sufficient to obtain a highly macroporous structured membrane. Highly percolating properties of these new A-PEI membranes make the material applicable in natural drainage systems. The high density of amine groups in composite membranes explain their high affinity for anions in acidic solutions. FTIR, SEM-EDX and XPS analysis are used to explore the sorption mechanism. Se(VI) is sorbed through electrostatic attraction between positive amine groups and negative selenium anions; in a second step, bound Se(VI) is reduced by amine and hydroxyl groups in acidic conditions. A-PEI membranes are successfully used for recovering Se(VI) anions at pH 2. The maximum sorption capacity is close to 83 mg Se g−1; the sorption isotherm is described by the Sips and Langmuir equations. The membranes are poorly sensitive to flow rate in the range 15–50 mL min−1. The kinetic profiles are fitted by the pseudo-first order rate equation. Solute desorption is operated using NaOH solutions; the sorbent shows a remarkable stability in sorption and desorption properties for a minimum of 4 cycles.