A global shallow water model with the double Fourier series as basis functions (SWM-DFS) is applied to the interaction and movement of typhoon-scale vortices. The numerical model incorporates a fourth-order spectral filter to surpress the small-scale numerical noises. The vortices are given axisymmetric and are initialized to be in the gradient wind balance. It is found that SWM-DFS well simulates the interaction between strong vortices with accuracy, and also the movement of a single vortex superimposed on the observed flow. We discuss the advantages of using global domain model instead of regional model in simulating the vortices interaction and movement on the sphere.