Orientation-averaged optical characteristics of single aerosol particles are needed for precise modeling of radiative processes in the Earth′s atmosphere. Optical properties of internal-mixed urban aerosols with the sulfate coated on black carbon are studied based on discrete dipole approximation for the size parameters from 0.1 to 25. Effects of the internal topology on particulate properties are also performed by changing the position of black carbon. Significant influences are observed for the extinction, scattering, backscattering efficiency factors, asymmetry parameters, extinction-to-backscattering ratios and single scattering albedos of the internal-mixed particles. These influences are relatively small for the size parameter less than 1 while those are large for size parameter more than 1. Meanwhile only the scattering phase function in Rayleigh scattering region and linear polarization in Rayleigh scattering region except the scattering angles near 0° and 180° are almost irrespective of the black carbon position. Smaller black carbon corresponds to weaker effects of black carbon positions on the extinction, scattering and backscattering efficiency factors. Shorter distance of black carbon from the boundary of mixtures with the same size parameter is accompanied by larger single scattering albedos and lower absorption efficiency factors associated with the lensing effect. Small black carbon or large size parameter has the more evident lensing effect related to internal-mixed particles with short distance of black carbon from the center of mixtures with the same size.