In this paper, we solve the classical Multi-agent Pathfinding (MAPF) problem. Existing approaches struggle to solve dense MAPF instances. In this paper, we propose a Corridor Generating Algorithm for MAPF, namely CGA-MAPF. In CGA-MAPF, the agents build \emph{corridors}, a set of connected vertices, from current locations towards agents' goals and evacuate other agents out of the corridors to avoid collisions and deadlocks. The proposed algorithm has a reachability property, i.e. every agent is guaranteed to reach its goal location at some point. In the experimental section, we demonstrate that CGA-MAPF outperforms baseline algorithms in terms of success rate across diverse MAPF benchmark grids, achieving state-of-the-art performance.