A new one-pot technique for preparation of polysaccharide-based Pd- and Pd-Ag nanocatalysts by sequential supporting natural polymer (2-hydroxyethyl cellulose (HEC), chitosan (Chit), pectin (Pec)) and metals on zinc oxide was developed. The nanocatalysts based on polysaccharide were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), Brunauer–Emmett–Teller (BET), infrared spectroscopy (IRS), X-ray powder diffraction (XRD), X-ray photoelectron spectra (XPS) and elemental analysis methods. The catalyst characterization results indicated complete adsorption of polysaccharide and metal ions on zinc oxide, forming polymer-stabilized Pd nanoparticles of ~2 nm in size, evenly distributed on the support surface. The catalysts were studied in the hydrogenation of 2-hexyn-1-ol under mild conditions (0.1 MPa, 40 °C). The catalysts demonstrated nearly the same conversion of 2-hexyn-1-ol. The selectivity to cis-hexen-1-ol of the catalysts decreases in the following order: 0.5%Pd-Ag(3:1)HEC/ZnO>0.5%Pd-Ag(3:1)Pec/ZnO>0.5%Pd-Ag(3:1)Chit/ZnO. The optimum reaction temperature and catalyst loading for the Pd-Ag catalysts modified with HEC and Chit have been determined (40 °C, 0.05 g).