In order to study the hydrodynamic process of a neck cutoff, on the basis of the field observational data of a meandering river at the Zoige Basin in the Yellow River source region, a numerical model is set up based on the incompressible Reynolds averaged Navier-Stokes equation, k-ε turbulent model, and finite volume method. Free surface is taken into consideration by σ coordinate transformation. Change of the flow diversion ratio, variation of the three dimensional velocity field, and the flow structures in the upstream and downstream were analyzed during the neck cutoff process. It shows that the flow diversion ratio and width-depth ratio gradually increases with the development of the neck cutoff and the widening of the new channel, revealing a positive linear correlation. Velocity field of the old bend channel is not affected at the initial stage of the neck cutoff. As the flow diversion ratio increases gradually in the new channel, the discharge, average water depth, and the mean velocity in the old channel decreases gradually, while the discharge in the new channel increases. Average water depth and mean velocity in the new channel shows a characteristic of first increase and then decrease. Neck cutoff does not change the velocity distribution in the upstream but has strong influence on the flow structure at the apex of the downstream bend.