Among various speed-sensorless control methods for induction motors(IMs), phase-locked loop(PLL)-based speed estimation schemes(SESs) have become attractive due to the advantages of easy implementation and good flexibility. However, most of the PLL-based schemes with the proportional-integral(PI)-based loop filter may lead to obvious performance degradation under acceleration and deceleration operation modes. To address this, in this paper, a four-consecutive-samples(FCS)-based SES is developed for IMs to achieve accurate estimation. The proposed SES uses the rotor flux and its delay signals, instead of solely increasing the system order. Additionally, considering the adverse effects of disturbances on the estimation performance of the proposed SES, a closed-loop flux observer(CLFO) that is able to provide high robustness against disturbances, is introduced to the proposed SES. The performance of the proposed SES is experimentally investigated on a case study system.