This article presents an active current sensor (CS) fault-tolerant control (FTC) strategy for induction motor (IM) drive with adaptation of rotor and stator resistances. The stator current estimator with online adaptation of resistance parameters was applied for the reconstruction of missing current signals. A model reference adaptive system (MRAS), based on a neural network (NN), was used to estimate the rotor resistance. Additionally, stator resistance estimation was applied based on ratio index. The use of such a solution allowed for a significant increase in the quality of stator current reconstruction, which is particularly important for the design of CS fault detection (FD) and compensation algorithms. A wide range of simulation studies have been carried out for different operating conditions of the IM drive. The results showed that applying rotor and stator resistance estimation can improve the quality of stator current estimation by up to approximately 95% under rated operating point. The study was carried out for nominal and low speeds, with two, one, and without healthy CS.