A series of core–shell-structured composite molecular sieves comprising zeolite single crystals (i.e., ZSM-5) as a core and ordered mesoporous silica as a shell were synthesized by means of a surfactant-directed sol–gel process in basic medium by using cetyltrimethylammonium bromide (CTAB) as a template and tetraethylorthosilicate (TEOS) as silica precursor. Through this coating method, uniform mesoporous silica shells closely grow around the anisotropic zeolite single crystals, the shell thickness of which can easily be tuned in the range of 15–100 nm by changing the ratio of TEOS/zeolite. The obtained composite molecular sieves have compact meso-/micropore junctions that form a hierarchical pore structure from ordered mesopore channels (2.4–3.0 nm in diameter) to zeolite micropores (≈0.51 nm). The short-time kinetic diffusion efficiency of benzene molecules within pristine ZSM-5 (≈7.88×10−19 m2 s−1) is almost retainable after covering with 75 nm-thick mesoporous silica shells (≈7.25×10−19 m2 s−1), which reflects the greatly opened junctions between closely connected mesopores (shell) and micropores (core). The core–shell composite shows greatly enhanced adsorption capacity (≈1.35 mmol g−1) for large molecules such as 1,3,5-triisopropylbenzene relative to that of pristine ZSM-5 (≈0.4 mmol g−1) owing to the mesoporous silica shells. When Al species are introduced during the coating process, the core–shell composite molecular sieves demonstrate a graded acidity distribution from weak acidity of mesopores (predominant Lewis acid sites) to accessible strong acidity of zeolite cores (Lewis and Brønsted acid sites). The probe catalytic cracking reaction of n-dodecane shows the superiority of the unique core–shell structure over pristine ZSM-5. Insight into the core–shell composite structure with hierarchical pore and graded acidity distribution show great potential for petroleum catalytic processes.