In order to improve the operating reliability of the brushless DC motor (BLDCM), a Hall sensor fault diagnosis and fault-tolerant control method based on the least square method is proposed. Using the least square fitting curve as the evaluation model of the first-order Taylor algorithm, the rotor position of the motor is accurately estimated, so as to realize the diagnosis of the faulty Hall sensor. The jump time lost under the fault of the Hall sensor is reconstructed by adopting the jump time of the normal Hall position sensor, and the least square fitting curve is obtained again. This method can realize the fault-tolerant control under the fault of Hall sensor，and effectively restrain the mechanical installation deviation to estimate the position error of the Hall sensor failure. The experimental results show that the proposed fault diagnosis method can quickly and accurately identify the fault Hall sensor, and the fault-tolerant control method can effectively ameliorate the system performance when the fault occurs.