We examined the shear stress in toluene-based suspensions of titanium dioxide nanoparticles/poly(vinylacetate) subjected to constant shear rates. The stress exhibited periodic oscillations at shear rates in a certain range. The amplitude of these oscillations first increased and then decreased with increasing ethanol concentration in the suspensions, indicating a transient stress response that was tunable by utilizing the solvent composition. In the oscillation mode, the suspensions showed a viscoelastic, shear-thickening behavior. The composition-dependent stress oscillation is discussed on the basis of hydrodynamic and depletion attractions among the particles.