For the low-speed instability problem of speed sensor-less vector control system of induction motor based on full-order flux observer, the unstable reason of observer at the low-speed generation region was analyzed by applying Popov's hyperstability theory, and a design criteria of feedback gain was proposed to stabilize the observer at low-speed mode. A stability analysis process was simplified based on rotor flux orientation and a multi-dimensional problem about the system poles stability was transformed into a one-dimensional problem about system zeros stability by using Routh-Hurwitz criterion. Furthermore, the stability condition of speed estimation system was derived and a design method of stability feedback gain was obtained. The simulation results show that the speed estimation system can work stably at a low speed of 50 revolutions per minute and a very low speed of 10 revolutions per minute. Compared with the traditional poles assignment approach, the system has better convergence and stability performance at low-speed generation region, and improves the dynamic and static performances of speed sensor-less vector control system at low-speed region.