The longitudinal coaming of the liquefied natural gas (LNG) carrier’s cargo tank dome is typically subjected to significant longitudinal loads during operation, leading to stress concentration and potential failure at the toe of the end bracket. To address this issue, a shape optimization study was conducted on the end bracket structure. The optimization process sequentially employed orthogonal experimental design, intuitive analysis, comprehensive experimental design, and a GA-BP-GA (Genetic Algorithm-Back Propagation-Genetic Algorithm) hybrid method for stepwise refinement. The results demonstrate that through shape optimization, the maximum stress of the bracket was reduced by 22.9% compared to the original design. The influence of various design variables on the maximum stress decreases in the order of horizontal arm length ( L), toe height ( h), and arc radius ( r). The introduction of dimensionless parameters C_L and C _r reveals that C_L exerts a greater influence on the maximum stress than C_r. A lower maximum stress is observed when the stress concentration is located at the arc edge. Furthermore, the optimal structural dimensions, which yield a lower maximum stress located at the arc edge, correspond to C_L values ranging from 1.15 to 1.25 and C_r values ranging from 1.1 to 1.3. The optimization design process, methodology, and related conclusions presented in this study can provide valuable references for the design of ship bracket structures.