Abstract: For the low-speed instability problem of speed-sensorless vector control system of induction motor, especially for ultra-low speed scenario, a new full-order adaptive observer algorithm was proposed. The newly-built algorithm consists of the improved feedback matrix algorithm and the speed adaptive law algorithm. By establishing an observer state error equation considering the nonlinear voltage error（NVE） of the inverter and the stator resistance voltage drop（SRVD）, the influence of NVE on estimated speed was analyzed, and then a feedback matrix that can reduce NVE of the inverter and the influence of SRVD on the speed estimation was developed. Meanwhile, the traditional adaptive law was improved by introducing a compensation amount, on the basis of traditional adaptive law, to compensate the flux error caused by the NVE of the inverter and the SRVD. In addition, it has the ability of self-adaptive to guarantee the satisfactory accuracy of speed estimation at low speed. This method has been validated by the 2.2 kW induction motor experimental platform. Experimental results show that the algorithm presented in this paper can guarantee the stable operation of the motor under the rated load and 180% rated load at low, ultra-low and 0 speed with good dynamic and static characteristics.