An algebraic multigrid (AMG) algorithm based on hybrid coarsening is proposed for the linear systems of the discrete pressure Poisson which is derived from the SIMPLE algorithm for the Navier-Stokes equations in complex flows. This algorithm combines a class of non-smoothed aggregation coarsening with classical C/F coarsening to construct grid hierarchy, hoping to reduce the cost in the setup phase of the AMG algorithm without affecting convergence. The high performance of the proposed algorithm is verified by numerical simulation of complex flow in the combustion chamber of aero-engine. The results show that the proposed algorithm can achieve 78% acceleration compared with the classical AMG algorithm.