In this paper, we derive in vector form the recursive aggregate T-matrix algorithm based on the principles of electromagnetic wave multipole expansion of vector spherical wave functions and the vector addition theorem. After that we establish a three-dimensional electromagnetic scattering model for multiple spherical scatterers by simulating the scattering of subsurface discrete random scatterers using the derived algorithm. Calculating the scattering from different sizes, randomly distributed spherical scatteres and analyzing the high-order scattering effects, we can conclude that the vector recursive aggregate T-matrix algorithm has a high computation accuracy, and contains the interaction effects among multiple scatterers, therefore we can calculate the total scattering effects accurately from multiple scatterers. The established model can be served as a powerful tool in applications for retrieving the impact caused by the scattering of subsurface discrete random scatterers in soil moisture from radar measurements.