In this paper, we study the interface and surface solitary waves on a two-layer fluid with basic currents. It is found that there are two modes of solitary waves, i.e., the fast mode and rhe slow mode, they are always governed by a KdV equation. The influence of currents on solitary waves is discussed. By using the two-fluid model, the themocline in ocean is studied, the long, weak nonlinear waves in a homogeneous density fluid with shear flow are studied also.