In order to investigate the flow state transition with two shear flows orthogonal to each other, we performed direct numerical simulations of Taylor–Couette–Poiseuille flow (TCPF), which is a combination of Taylor–Couette flow and axial pressure gradient drive. It is known that the Taylor vortex appears in a Taylor–Couette flow, under the supercritical transition conditions of inner-cylinder rotation only and co-rotation of both cylinders (Taylor, 1923). However, in TCPF, we found that the flow state transition process for the Reynolds number of these two conditions, which are based on the same phenomenon, undergoes different flow state transitions. For the first condition with only inner-cylinder rotation, we observed that the Taylor vortex weakens as the axial flow increases, resulting in completely laminar flow. However, the flow field becomes unstable again, and the helical turbulence observed in the subcritical transition of the annular Poiseuille flow without cylinder rotation appears (Ishida, 2016). In the second case, we observed that the Taylor vortex is noisy as the axial flow increases, and the checkerboard-like structure is transformed into a stripe-like structure, leading to turbulence.