Under harsh service conditions and complex loading environments, gearbox cases in aero-engines are required to be both structurally robust and lightweight. A key design challenge is balancing weight reduction with control of bearing bore misalignment, which is an important performance metric. To address this issue, a topology optimization method for the gear transmission case is proposed, considering both mechanical and inertial loads. The approach is based on the solid isotropic material with penalization(SIMP) interpolation model. Inertial load effects on attached components are incorporated into the optimization model, which imposes constraints on case stress, critical bearing bore misalignment, and volume fraction of the optimized region. The objective is to minimize the weighted structural compliance of the case under multiple loading conditions. The proposed method achieves a 7.1% reduction in case weight and simultaneously decreasing maximum von Mises stress, total deformation, and critical bearing bore misalignment by 7.1%, 3.1% and 11.1%, respectively.