Abstract: In this paper, by using a three-layer model and the observations from Satellite ISEE, the stabilities of rotational discontinuity for magnetopause are discussed. The results show that: (1) a kind of instability may be excited in the magnetopause rotational discontinuity, the growth rate of the instability increases as the wave number k increases; (2) when the interplanetary magnetic field is northward, the magaaetopause rotational discontinuity is stable; when the interplanetary magnetic field becomes southward gradually, the growth rate of the instability increase rapidly; (3) when the velocity of solar wind is larger, the growth of rate of instability is larger correspon-dently; (4) when the interplanetary magnetic field is southward, the growth rate of instability increases rapidly as the angle between the interplanetary magnetic field and the tangential surface of the magnetopause increases.