A set of studies have made it possible to develop a method for the synthesis of high-silica zeolite NaY-FS, which has a high adsorption capacity and a developed secondary porous structure. The method involves mixing kaolin with powdered zeolite NaY, polyvinyl alcohol (PVA), and fumed silica (FS) in an amount to have the total content of components in the mixture as follows (wt %): zeolite NaY (molar ratio SiO2/Al2O3 = 5.5-7.0) 55-70, PVA 1-2, fume silica 37, and kaolin the rest; moistening and stirring the mixture until a homogeneous mass, shaping granules; their calcining; hydrothermal crystallization in a sodium silicate solution from reaction mixtures with the composition (2.43.6) Na2O Al2O3 (1012) SiO2 (180220) H2O; and washing and drying the granules. In addition, the crystallization kinetics of zeolite NaY-FS from the reaction mixtures of these compositions has been studied.