Based on the vector angular spectrum of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Airy-Gaussian beam in the far field has been presented. According to the analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam in the far field are investigated respectively. The formulas obtained are applicable not only in the paraxial case, but also in the nonparaxial case. The physical pictures of Airy-Gaussian beams are well illustrated from the vectorial structure, which may provide a new approach to manipulate laser beams.