In this talk, we investigate the two-dimensional Patlak-Keller-Segel-Navier-Stokes system perturbed around the Poiseuille flow $(Ay^2, 0)^\top$ and show that the solutions to this system are global in time if the Poiseuille flow is sufficiently strong in the sense of amplitude $A$ large enough. This seems to be the first result showing that the Poiseuille flow can suppress the chemotactic blow-up of the solution to chemotaxis-fluid system. Our proof will be based on a weighted energy method together with the linear enhanced dissipation established by Coti Zelati-Elgindi-Widmayer (Commun. Math. Phys. 378 (2020) 987-1010). This is a joint work with Dr H Li and Professor X Xu.