Transient electromagnetic pulse (EMP) can easily couple into equipments through small apertures in its shells. To study the coupling effects of transient Gauss pulse to a cubic cavity with openings, coupling course is simulated using sub-gridding finite difference in time domain (FDTD) algorithm in this paper. A new grid partition approach is provided to simulate each kind of apertures with complex shapes. With this approach, the whole calculation space is modeled, and six kinds of aperture with different shapes are simulated. Coupling course is simulate in the whole time domain using sub-gridding FDTD approach. Selecting apertures with dimension of several millimeters to research, coupled electric field waveform, power density and coupling coefficient are calculated. The affect on coupling effects by varied incident angle and varied pulse width are also analyzed. The main conclusion includes interior resonance phenomenon, increase effect around rectangle aperture and several distributing rules of coupled electric field in the cavity. The correctness of these results is validated by comparing with other scholars’ results. These numerical results can help us to understand coupling mechanism of the transient Gauss pulse.