The flow between two concentric cylinders, with the inner one rotating and with an imposed pressure-driven axial flow, is studied using numerical simulation. The case without the axial flow was investigated in the preceding paper. This study considers the identical flow geometry as in the experiments of Wereley and Lueptow[Phys. Fluid, 11(12), 1999]. They carried out experiments using PIV to measure the velocity fields in a meridional plane of the annulus in detail. When an axial flow is imposed, the critical Taylor number is increased. The axial flow stabilizes the flow field and decreases the torque required to rotate the inner cylinder. The velocity vector fields obtained also show the same flow features found in the experiments of Wereley and Lueptow.