To selectively adsorb dimethyl disulfide (DMDS) from its competition components, such as methyl tert-butyl ether (MTBE), the shell layer of silicalite-1 crystals was synthesized on a commercial Y zeolite crystal surface (CuYH@silicalite-1 core-shell structured composites) with a mass composition of tetraethyl orthosilicate/tetrapropylammonium hydroxide/ethanol/H2O/CuYH = 20 g (0.096 mol):19 g (0.0234 mol):17 g (0.369 mol):87 g (4.829 mol):5 g. CuYH zeolites were acquired by ion-exchanging Cu2+ with HCl-treated NaY (noted as NaYH). Results showed that by the dealuminization of HCl, the ratio of Si/Al for NaY zeolites was dramatically increased, providing NaYH a favorable condition for growth of silicalite-1 coatings, and many vacancies left by dissolved Al also enlarged the outside surface area of NaYH to provide more load locations for silicalite-1 crystals. Among all these synthesized adsorbents, the core-shell Y-H-CuCl2 displayed the best DMDS adsorption of approximately 34.585 mg(s)/g(adsorbent) in MTBE solution and a 100% desulfurization rate for approximately 3 h. Also, the process of synthesizing CuYH@silicalite-1 core-shell composites and their shape-selective adsorption were detailed.