Abstract: The common LMS (least mean square) adaptive filtering algorithm is difficult to harmonize three performance indices, i.e. initial convergent speed, time-varying track ability, and constringent precision, while modeling the system. In order to solve this problem a region-varying and step size-varying LMS algorithm was put forward, and its algorithmic astringency was proved by the Lyapunoy Function. It is shown that the algorithm gives attention to the three performance indices above and can be applied to modeling the system and the inverse system in a field of control.