The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, which takes into account hydrodynamic interactions and thermal fluctuations accurately. Simulations were performed under steady shear flow with periodic boundary conditions in the three directions. The apparent shear viscosity of the dispersions was calculated at volume fractions ranging from 0.31 to 0.56. Shear-thinning behavior was clearly observed at high volume fractions. The low- and high-limiting viscosities were then estimated from the apparent viscosity by fitting these data into a semiempirical formula. Furthermore, the short-time motions were examined for Brownian particles fluctuating in concentrated dispersions, for which the fluid inertia plays an important role. The mean square displacement was monitored in the vorticity direction at several different Peclet numbers and volume fractions so that the particle diffusion coefficient is determined from the long-time behavior of the mean square displacement. Finally, the relationship between the non-Newtonian viscosity of the dispersions and the structural relaxation of the dispersed Brownian particles is examined.