The discrete dipole approximation (DDA) method is used to study the light scattering properties of a soot cluster which adheres to a large particle with different sizes and material composition. The numerical results of the scattering intensity and the degree of linear polarization for a wide variety of complex soot aggregates in random orientation are illustrated, and the effects of the material composition and the size of the large particle on light scattering properties of complex soot aggregates are analyzed. It is shown that the material composition and the size of the large particle can strongly influence or even dominate the overall light scattering properties of the aggregates.