Under low PWM-to-output frequencies ratio conditions, the performance of the discrete adaptive full-order observer (DAFO) deteriorates sharply with the forward Euler (FE) method. This seriously affect the stability of speed sensorless induction motor (IM) drives. To address the problem, this paper proposes an improved DAFO with the "prediction-correction" method. The studied method can improve the discretization accuracy of the observer. Compared with the conventional DAFO, the proposed DAFO ensure stable operation at low PWM-to-output frequencies ratio. The experimental results from a 3.7kW IM drive system verify the effectiveness of the studied observer.