The deformation and breakup processes of particle-cluster aggregates of unequal-sized particles under shear flows were investigated numerically using the two-phase lattice Boltzmann method. The diameter of the larger particles was taken as double that of the smaller particles, and the van der Waals attraction force was taken into account for the interaction between the particles. Also, the Brownian force was applied to each particle in order to treat Brownian motion. Simulations were performed for various fluid forces acting on the particles and various inter-particle forces. Key parameters for estimating the dispersion of the aggregated particles were found to be the ratios of fluid force to the maximum inter-particle force, Y-11 (between small particles), Y-12 (between small and large particles), and Y-22 (between large particles), and also the Peclet number, which is the ratio of the rate of diffusion by shear flow to the rate of diffusion by Brownian motion, Pe(1) (small particle) and Pe(2) (large particle). Thus, the aggregate of non-Brownian particles is dispersed when Y-max (the largest among Y-11, Y-12, and Y-22) is also over 0.002. In addition, the aggregated disperses to individual particles when Y-min (the smallest among Y-11, Y-12, and Y-22) is also over 0.002. Comparison of the calculated results of the dispersion of Brownian and non-Brownian particles indicated that Brownian motion retards the dispersion of small particles but promotes the dispersion of large particles. The effect of Brownian motion is remarkable when the Peclet number is under 10(4). The results obtained were compared with the results for the dispersion of aggregates of the same-sized particles (Nishiyama et al., submitted). The threshold value of Y for the dispersion in the present paper (polydispersion) was approximately the same as that for monodispersion, but the effect of Brownian motion is not the same as that for monodispersion. The effect represents not only the retardation of the dispersion (small particles) but also the promotion of the dispersion (large particles).