To obtain the time evolution of the local scour of bridge piers and to explore the scouring characteristics of piers with different cross sections, the user-defined function and the dynamic mesh updating technique of the computational fluid dynamics software FLUENT were used. The bed shear stress considering the enhancement effect of turbulence vortex and the critical shear stress considering the influence of the bed slope were calculated to obtain the sediment transport rate. The dynamic variation of bed topography with time was achieved by the relationship between sediment transport rate and bed elevation. Simulation distortion and numerical instability caused in the condition that the bed slope is greater than the sediment repose angle can be overcome through the adjustment of sediment collapse. It shows that the maximum scour depth, the shape of the scour hole and the flow structures by numerical simulation are in good agreement with the experimental results. With the same maximum pier width, the scour depth of the streamlined piers is about 45% and 40% lower than that of the round-ended piers and the sharp-nosed piers respectively, and the range of the scour hole is also reduced.