A transient process of the Reynolds-stress distribution due to a change of the bed shear stress in an open channel flow is investigated and a relaxation model, or a convolution-integral model with a concept of an impulse response, is proposed. The impulse response of the Reynolds-stress distribution for the change of bed shear stress is determined by a classic wind-tunnel data for air flow under transition due to an abrupt change of bed roughness, and it is successfully applied to the open channel data of flow with an abrupt change of bed roughness without any modification of a relaxation parameter of the model. Furthermore, the applicability of the proposed model is inspected by the transient properties of the velocity profile and the turbulence intensities obtained from the flume experiments for open channel flows with spatially acceleration or deceleration.