Abstract: To suppress the blow-up phenomenon in the solution of the parabolic-parabolic Keller-Segel equation, Poiseuille flow is introduced and the Bootstrap method is primarily used to prove the global existence of the system’s solution when the amplitude A is large enough. First, the Keller-Segel equation with Poiseuille flow is subjected to a time scaling transformation, and the system is decomposed into zero-mode and non-zero-mode components using the orthogonal projection operator P. Then, an energy functional is introduced, and energy estimates are employed to establish zero-mode and non-zero-mode estimates for the microbial density n and chemical concentration c. These estimates are further used to improve the energy functional, and the Moser-Alikakos iteration method is applied to obtain improved estimates for n in the L^∞L^∞ space. Finally, by combining the blow-up criteria of the system with the Bootstrap method, it is confirmed that sufficiently strong Poiseuille flow can indeed suppress the blow-up phenomenon of the parabolic-parabolic Keller-Segel equation in a finite channel. In particular, an extra smallness assumption on the initial chemical gradient is needed to control the mixing destabilizing effect.