The direct deposition of polyethyleneimine (PEI), a weak polycation with a large content of amino groups, onto sand fractions with different sizes (F70, F100, F200, and F355), resulted in versatile core-shell sorbents for water cleaning. Herein, PEI and the weak polyanion poly(acrylic acid) (PAA) were directly precipitated as an nonstoichiometric polyelectrolyte complex ([PEI]:[PAA] = 2:1) onto a sand surface followed by cross-linking with glutaraldehyde (GA) at three molar ratios ([CHO]:[amine] = 1:10; 1:5; 1:1 = r). Non-crosslinked polyelectrolyte chains were washed out in strongly basic (pH 14) and acidic (pH 0) media. The sand/PEI-GA composites were evaluated to determine the organic shell stability using swelling experiments and X-ray photoelectron spectroscopy. The sorbed/desorbed amount of two model pollutants (copper ions and bromocresol green) in column experiments depended on the sand fraction size and cross-linking degree of the PEI shell. The maximum recorded values, after five loading/release cycles of pollutant species onto F70/PEI-GAr, F100/PEI-GAr, F200/PEI-GAr, and F355/PEI-GAr, were situated between the 0.7–5.5 mg Cu2+/mL column and 3.7–15 mg BCG/mL column. Sand/PEI-GAr composites could act as promising sorbents, low-cost and eco-friendly, which could be applied for water purification procedures.