Bending river is the most common river type in nature, and it is also a typical example for river evolution. The transform of the flow pattern can affect the development of the riverbed form. In return, the variation in the riverbed form can affect the hydrodynamic characteristics of the flow, thereby leading to the continuous evolution of the bending river. Based on this, a theoretical model for the bending river is established. The hydrodynamic instability characteristics of the laminar flow in the channel with a variable curvature, a typical model as the meandering river, are studied,and the variations of some parameters such as the curvature, the wave number, and the wave frequency are also discussed. Bending river is the most common river type in nature, and it is also a typical example for river evolution. The transform of the flow pattern can affect the development of the riverbed form. In return, the variation in the riverbed form can affect the hydrodynamic characteristics of the flow, thereby leading to the continuous evolution of the bending river. Based on this, a theoretical model for the bending river is established. The hydrodynamic instability characteristics of the laminar flow in the channel with a variable curvature, a typical model as the meandering river, are studied, and the variations of some parameters such as the curvature, the wave number, and the wave frequency are also discussed.