Rheological behaviors and microstructures of aqueous suspensions of a bimodal core-shell type of carboxylated particles have been studied by varing a weight ratio of two particles. Diameters of these particles in the fully neutralized state were 176nm and 291nm, respectively. Steady shear flow was measured with a coni-cylinder rheometer, and the critical shear stress σc, defined as the stress at the transition point from Newtonian flow to shear thinning flow, was estimated. The distance ξ which is the center to center distance between neighboring particles in an ordered structure of the suspensions was estimated with the small angle X-ray scattering (SAXS) method. All suspensions tested exhibited psudoplatic flow and gave single diffraction peak in their SAXS profiles. This result suggests that an alloy structure made of the bimodal particles is formed in these suspensions. As a weight fraction of large particle increased, viscosity and a degree of shear-thinning of the suspension decreased, and also ξ decreased. The relationship between σc and ξis represented as σc=4kT/3πξ3. This indicates that σc is dominated by thermal motion of lattice of the ordered structure. These findings indicate that the shear-rate dependence of the viscosity of the suspension is attributed to dynamical competition between the thermal motion and the hydrodynamic motion under shear flow, and the mechanism is applied to not only uni-modal suspensions but also bimodal suspensions.