Highly accurate Boussinesq-type equations in terms of velocity potential are used for the simulation of shallow-water sloshing in a three-dimensional tank under the framework of the potential flow theory. The total velocity potential is separated into two parts: one part is a particular solution which satisfies the Laplace equation in the fluid domain and the no-flow condition on the walls while the other part is solved by the Boussinesq-type model. In the process of numerical calculation, the finite difference method is used for spatial derivative discretization and the 4th Runge-kutta method is used for time iteration. To verify the numerical model, the aspect ratio of the tank is set to be much less than 1 for simulation of 2D cases and is compared with the results published. In the 3D cases, four different sloshing motion forms are observed at each external excitation frequency, and a corresponding number of traveling waves are observed on the free surface. Moreover, the effects of external excitation frequency and coupling excitation on the sloshing motion in the tank are discussed.