The structural design of a composite bracket applied to an aircraft propulsion system was carried out in this study. Aircraft engine intakes are fitted with various components in order for the engine to operate. The thickness of the composite laminate was determined through classical laminate theory. The mechanical properties of the manufactured specimen were analyzed and reflected in the conceptual design. The material for the design and analysis was a composite material consisting of carbon fiber and epoxy resin. The results of the designed composite structures were compared with those of aluminum alloy structures, and the structural integrity was investigated via the structural analysis of the designed bracket. The commercial FEM code Nastran 2022 and ANSYS 2023 software were used for numerical analysis. A stress and deformation analysis was carried out, and the buckling stability was also evaluated due to the characteristics of the composite structure. The bracket was shown to be sufficiently safe through structural analysis.