A principle of selecting relaxation parameter was proposed to observe the limit computational capability of the incompressible LBGK models developed by Guo ZL (Guo model) and He SY (He model) for high Reynolds number flow.To the two-dimensional driven cavity flow problem, the highest Reynolds numbers covered by Guo and He models are in the range 58000-52900 and 28000-29000, respectively, at 0.3 Mach number and 1/256 lattice space. The simulation results also show that the Guo model has stronger robustness due to its higher accuracy.