To predict the resonance frequency of the real liquefied natural gas (LNG) tank, a Cartesian grid based three-dimensional (3D) multiphase flow model is used to simulate violent sloshing in a prismatic tank at different filling levels and excitation frequencies. In this model, a semi-implicit finite difference method is adopted to solve the incompressible two-phase flow Navier-Stokes (N-S) equations on a staggered Cartesian grid. Besides, a radial basis function ghost cell method (RBFGCM) is used to treat the irregular tank walls and a 3D gradient-augmented level set (GALS) method is used to capture highly nonlinear free surfaces. Based on the present model, the violent sloshing induced by rolling excitations in the 3D prismatic tank is simulated. Satisfactory convergences of grid sizes and time steps demonstrate the high accuracy and reliability of the present method. Moreover, the present results of the impulsive pressure and wave elevation agree well with the experimental data for different filling water depths. In addition, violent sloshing phenomena are captured such as wave rolling. Furthermore, the relationship between the pressure amplitude on the tank wall and the excitation frequency at four filling levels are investigated to identify the resonance frequency of the prismatic tank, to provide theorical guides for structrual design of the tanks.