With the rapid development of robot swarm technology and its diverse applications, navigating robot swarms through complex environments has emerged as a critical research direction. To ensure safe navigation and avoid potential collisions with obstacles, the concept of virtual tubes has been introduced to define safe and navigable regions. However, current control methods in virtual tubes face the congestion issues, particularly in narrow ones with low throughput. To address these challenges, we first propose a novel control method that combines a modified artificial potential field (APF) for swarm navigation and density feedback control for distribution regulation. Then we generate a global velocity field that not only ensures collision-free navigation but also achieves locally input-to-state stability (LISS) for density tracking. Finally, numerical simulations and realistic applications validate the effectiveness and advantages of the proposed method in navigating robot swarms through narrow virtual tubes.