This paper presents a fault tolerant control (FTC) based on Radial Base Function Neural Network (RBFNN) using an adaptive control law for double star induction machine (DSIM) under broken rotor bars (BRB) fault in a squirrel-cage in order to improve its reliability and availability. The proposed FTC is designed to compensate for the default effect by maintaining acceptable performance in case of BRB. The sufficient condition for the stability of the closed-loop system in faulty operation is analyzed and verified using Lyapunov theory. To proof the performance and effectiveness of the proposed FTC, a comparative study within sliding mode control (SMC) is carried out. Obtained results show that the proposed FTC has a better robustness against the BRB fault.