Wireless LANs, which consist of access points and wireless stations, have widely spread in recent years. Routing in wireless LANs suffers the problem that each wireless station selects an access point and a wired path to its destination station. It is desired to design an adaptive routing protocol for wireless LANs since throughputs of communications are dynamically affected by selections of other wireless stations and external environmental changes. In this paper, we propose a routing protocol for wireless LANs based on attractor selection. Attractor selection is a biologically inspired approach, and it has high adaptability to dynamic environmental changes. By applying attractor selection, each wireless station can adaptively select its access point and wired path with high throughput against environmental changes. In addition, we design the protocol with a new technique: combination of multiple attractor selections. The technique is useful because it enables us to divide a problem into several simpler problems. To the best of our knowledge, our protocol is the first one designed around a combination of multiple attractor selections. We show the effectiveness and adaptability of our protocol by simulations.