In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed estimation strategy based on the current sensor fault-tolerant control is proposed to improve the speed estimation accuracy under the current sensor faults. First, to detect the current sensor faults in real time, the sequential probability ratio test is introduced to the system by using the innovations of the extended Kalman filter (EKF). Second, to ensure speed estimation accuracy, a double-cascading second-order generalized integrator (DSOGI) is employed to reconstruct the faulty current information when a fault is identified. Finally, the reconstructed current information is fed back to the sequential probability extended Kalman filter (SPEKF), which estimates the rotor speed of the IM, and high-accuracy speed estimation under the condition of current sensor faults is achieved. The effectiveness of the proposed strategy is validated by a series of experiments, which were conducted on a 3 kW induction motor drive platform.