It is well known that the operation of a speed-sensorless induction motor drive at zero stator current frequency is unstable theoretically if signal injection is not used. In this paper, the unstable reason is analyzed. The error between the stator input voltages of the adaptive full-order observer and motor is introduced for the operation at zero stator current frequency without any signal injection. When the stator current frequency is reduced to zero, the traditional speed estimation fails to estimate the rotor speed, but the rotor speed can be estimated by the proposed stator input voltage error. The stability of the proposed method is analyzed. Although the unstable problem at zero stator current frequency can be solved by the proposed method, there is a disadvantage that an error between the estimated and actual rotor speeds is caused. Finally, the feasibility of the proposed method is verified by experiments.