Furfural is a renewable lignocellulose-derived platform molecule, which can be transformed into biofuels and value-added chemicals (e.g., furfuryl alcohol and 2-methylfuran over metal-supported catalysts). Despite a number of approaches proposed for designing hydrogenation catalysts, highly selective furfural hydrogenation towards furfuryl alcohol (FA) or 2-methylfuran (2-MF) is still challenging. Here, we report on selective transformation of furfural either to FA or 2-MF achieved over zeolite BEA-supported Rh catalysts by optimizing Si/Al ratio and charge-balancing cations of the support. Among studied H- and Na-exchanged aluminosilicate BEA zeolite supports (Si/Al = 12.5; 25; 68; 150), Rh@Na-BEA catalysts lacking Brønsted and strong Lewis acidity showed enhanced selectivity towards FA (75 – 94% depending on the Si/Al ratio) at 74 – 84% conversion of furfural. In turn, selective formation of 2-MF (98% selectivity at 87% conversion) was observed over Al-rich Rh@H-BEA catalyst (Si/Al=12.5) with the highest concentration of Brønsted acid sites. Weaker adsorption of FA on Na- vs. H-form of Rh@BEA-12.5 catalyst was verified by FTIR spectroscopy and is assumed a key factor governing selective hydrogenation of furfural to FA over Rh@Na-BEA catalysts.