To verify the feasibility of the numerical methods and solution strategies for simulating the flows around bluff bodies controlled by steady suction, the separation and reattachment over a suctioncontrolled backwardfacing step (BFS) flow is numerically investigated using the dynamic kinetic energy subgridscale model (DKEM) model based on the large eddy simulation (LES) method and the SST k-ω model based on the Reynolds averaged NavierStokes (RANS) method, respectively. Comparisons of the mean pressure coefficient and reattachment length between the numerical simulations and the existed experiment are also conducted to prove the validity. The results indicate that the LES can acquire exact results under the refined grid adopted in the paper. Suction control with any suction flow coefficient C^Q can reduce the recirculation zone and reattachment length, and thus improve the flow fields downstream the step. With the increasing increments of the absolute C^Q,the effect of suction control is more significant. 