A fullorder observer with speed selfadapting rule of induction motor was presented. A strategy of restarting at unknown speed based on Popov stability theory was proposed. In the proposed strategy, the error between estimated speed and real speed was reflected. In order to make the estimated speed follow real speed rapidly, a method searching from middle of max motor speed to two sides was used. In addition, a method of preexcitation was used to decrease current impact during restart the motor at unknown speed. The correctness and effectiveness of the proposed strategy were proved by simulation results.