To achieve lightweighting of the aircraft landing gear door hinge under opening and closing loads, a topological optimization model based on the variable density method was established, with structural stiffness as the constraint and minimum mass as the objective. The hinge was redesigned according to the optimized configuration, and the stiffness and strength of the design area were validated. The original aluminum alloy hinge material was replaced with lower-density polyetheretherketone (PEEK), which can be fabricated into complex structures via fused deposition modeling (FDM), thereby enhancing design freedom for topology optimization. However, FDM-printed PEEK's mechanical properties are influenced by printing parameters. This study conducted tensile tests on PEEK specimens printed with different FDM parameters (e.g., layer height, platform temperature, and infill pattern). The optimal printing parameters were determined as 0.1 mm layer height, 120 °C platform temperature, and tetrahedral infill. Subsequently, the best-performing specimens underwent heat treatment, and the effects of different annealing parameters on tensile strength were investigated. The results showed that annealing at 330 °C for 2 hours yielded the highest strength improvement. Furthermore, the hinge's loading conditions during door operation were simulated via multi-body dynamics analysis, while static simulations under peak loads identified stress concentration areas. Topology optimization was then performed to minimize material usage while maintaining mechanical performance, achieving the lightweight goal.