The shaft bushings in many machines form a Taylor-Couette system with a thin clearance. The flow in such a clearance was studied in this paper by means of CFD simulation. Two different gap width ratios have been chosen to investigate the flow from laminar to turbulent range. Based on the simulation results a critical gap width ratio is determined in the turbulent regime, which is of importance to the transition of a turbulent flow with Taylor vortex in a turbulent flow without Taylor vortex.