When the finite difference time domain (FDTD) method is used to solve electromagnetic scattering problems in Schwarzschild space-time, the Green functions linking source/observer to every surface element on connection/output boundary must be calculated. When the scatterer is electrically extended, a huge amount of calculation is required due to a large number of surface elements on the connection/output boundary. In this paper, a method for reducing the calculation workload of Green function is proposed. The Taylor approximation is applied for the calculation of Green function. New transport equations are deduced. The numerical results verify the effectiveness of this method.