The inertial characteristics of aircraft fuel are the key factors affecting the maneuverability and safety of aircraft. Godunov smoothed particle hydrodynamics (GSPH) has great advantages in simulating strong nonlinear fluid structure interaction problems such as fuel sloshing and splashing, but there are still some problems of field pressure oscillation. Therefore, this study proposes a numerical improvement method combining GSPH with weighted essentially non-oscillatory (WENO) scheme to achieve high-precision simulation of fuel sloshing inertia characteristics. In this method, WENO reconstruction is integrated into the GSPH framework, and the pressure oscillation and numerical dissipation caused by strong sloshing are effectively reduced by the second-order Taylor-based stencil interpolation technique. At the same time, in order to accurately distinguish the surface particles from internal particles, the free surface detection method based on the velocity divergence field is applied, which provides the interface definition for inertial force calculation. Two benchmarks of dam break and tank sloshing are studied to verify the method. The numerical results are in good agreement with the experimental results in terms of free surface morphology and dynamic pressure distribution, which proves the validity of the method. On this basis, a set of codes accelerated by GPU is developed, the typical fuselage tank structure model is selected, and the transverse oscillation and rotation conditions are simulated according to the aviation standards. The influence of filling ratio and excitation parameters on fuel inertial characteristics is systematically analyzed. The results show that with the increase of the filling ratio, the offset of the center of gravity and polar moment of inertia caused by the fuel sloshing during rotation increases significantly. The influence of oscillation on inertial characteristics can be ignored; While under rotation, strong nonlinear sloshing occurs, and the amplitude of polar moment of inertia is significant.