In this paper, the FLUID characteristics of pitching SLOSHING under microgravity condition are investigated. A numerical method by solving the Navier-Stokes equations to study three-dimensional (3-D) nonlinear liquid SLOSHING is developed with OpenFOAM, a Computational FLUID Dynamics (CFD) tool. The computational method is validated against existing experimental data in rectangular tank under ordinary gravitational field. However under low gravity conditions, the SLOSHING liquid shows seemingly chaotic behavior and a considerable volume of liquid attaches on the sidewall due to the effect of surface tension, which is verified in simulation experiment. Besides, the nonlinear liquid behaviors in hemi-spherically bottom tank are firstly studied in this paper. It is found that the wave evolution becomes divergent with the decrease of gravitational acceleration. The natural frequency reaches a constant magnitude quickly with the increase of liquid height and then increases again until the filling level exceeds 70%. Meanwhile, the liquid dynamics of forced pitching SLOSHING under resonant and off-resonant condition are demonstrated respectively. The numerical techniques for 3-D simulation are hopeful to provide valuable guidance for efficient liquid management in space.