In wireless LAN, several terminals could share a single communication channel by using an appropriate media access control (MAC) mechanism. However, existing MAC schemes for wireless LAN have serious drawbacks such that it significantly degrades the throughput if it frequently occurs a collision of frames or a useless assignment of communication bandwidth. In this paper, we propose a new MAC scheme for wireless LAN to realize an efficient utilization of the communication bandwidth while suppressing the probability of frame collisions. The basic idea of the scheme is to conduct a channel assignment for each group which is dynamically constructed based on the unique identifier that is assigned to each terminal beforehand. The scheme could be customized by appropriately tuning parameters according to the given communication environment. The effect of the scheme is estimated by simulation. By the result of simulations, it is confirmed that the proposed scheme could achieve a stable performance for any access frequency.