The failure mechanism of composites dominates the matrix, fiber and interface, and in general, the matrix corresponds to the definitive cause of damage. A filament–wound composite structure involves a notable bridging effect owing to the matrix between the layers, and particle additives are generally adopted to strengthen the matrix. However, particle additives exhibit a low performance when applied to structures, owing to the dispersibility and particle agglomeration. In this study, the strengthening performance of carbon nanotube (CNT)/epoxy interleaves was experimentally verified to facilitate their implementation in the structural design of a filament–wound cylinder structure. The burst pressure, compression, bending and interfacial bonding strength of the cylinder improved by approximately 20%, 161%, 16% and 36%, respectively, and the positioning of CNT/epoxy interleaves was a more notable influencing factor compared to the proportion of CNTs in the entire winding layer. The number of macro voids decreased inside the epoxy modified CNT. The findings demonstrated that the incorporation of CNTs through CNT/epoxy interleaves could facilitate the matrix strengthening and enhance the interfacial bonding.