Based on fractal theory, the Monte Carlo method is used to simulate the structures of fractal soot aggegates in random distribution. The radiative properties of randomly distributed soot aggregates are studied using the discrete dipole approximation (DDA), and the effects of the fractal dimension ,the monomer diameters , the number of monomers in the soot aggregates and the refractive index on the radiative properties of aggregated soot particles are analyzed. The results show that the radiative properties of randomly distributed soot aggregates of a given fractal dimension are complex functions of the monomer diameters, the number of monomers in the aggregates,and the refractive index. For small values of the monomer diameters, the absorption cross section of soot aggregates tends to be relatively constant when the fractal dimension is small, but increases rapidly when the fractal dimension exceeds two. However, a monotonical reduction in light absorption with the increase of the fractal dimension is observed for soot aggregates with sufficiently large monomer diameters, number of monomers,and refractive index. The scattering cross section , extinction cross section and single-scattering albedo increase monotonically with the increase of the fractal dimension. In a word, the results for soot aggregates differ profoundly from those calculated for the equivalent spherical particles, and the discrepancies between them change litte with the increase of the fractal dimension.This research is of scientific value in studying the radiative properties of aerosols and their climatic effects.