Black carbon (BC), also known as soot, is one of the most important aerosols, and has a significant effect on the atmosphere and climate by scattering and absorbing both solar radiation and terrestrial emission. The complex cluster configured BC are usually treated as fractal aggregates with same-sized monomers, because the monomers are thought to have a narrow size distribution. However, some studies show the monomer diameters may vary from 10nm to 60nm, and obey a lognormal distribution. We investigate the optical properties of soot aggregates with different-sized monomers, and compare them with those of same-sized ones. The fractal aggregates are numerically generated by the cluster-cluster diffusion-limited aggregation (CDLA) algorithm, and the Generalized Multi-particle Mie (GMM) method is used to simulate the scattering and absorption properties. The key optical properties, such as extinction, scattering, and absorption cross sections, single scattering albedo and phase matrix, of the aggregates have normal distribution with large standard deviations, which are mainly a result of the monomer size distributions. It would require to average over 50 aggregates with different monomer size realizations and aggregates configurations to represent the ensemble-averaged optical properties of aggregates with given parameters. Similar phase matrix elements are obtained for the aggregates with different-sized and those with same-sized monomers. The aggregates with different-sized monomers exhibit much stronger scattering and absorption than the same-sized monomer aggregates with the geometric or arithmetic mean diameters. The influence of the geometric deviations for the monomer size distributions on the scattering and absorption is also investigated and discussed.