Flowing colloidal suspensions, such as blood and milk, are of crucial importance in our life as well as in a wide variety of industrial applications. However, elucidating their widely varying rheological properties at a microscopic level remains a challenge. In particular, the role of particle interaction has not been well understood. Using neutron scattering complemented by computer simulation and rheological measurement, we demonstrate that the rate-dependent flow behavior of a charge-stabilized colloidal suspension is a consequence of localized elastic response generated by particle interaction. The body of colloids under shear behaves like an elastic solid at short distances but like fluid at long distances. The short-lived, localized elastic region, transient elastic zone, plays a crucial role in determining the observed rheological behaviors. Our findings shed new light on understanding the nature of nonlinear rheology of soft matters with strong interactions. ; Comment: 24 pages,9 figures