The sustained oscillation of rotor speed is often experienced in PWM inverter induction motor (IM) drive systems. In this paper the oscillation is investigated from the point of view of Hopf bifurcation theory. The sufficient and necessary conditions for existence of limit cycle are introduced to determine the bifurcation set in the stator voltage versus stator frequency plane. According to the conditions it is clarified that the bifurcation set inherently exists in the instable operation of IM. Moreover, it is numerically shown that the V/f curve can be adjusted to stabilize the sustained oscillation of rotor speed.