Fault-tolerant control (FTC) solutions are increasingly being used in modern drive systems with AC motors. Such systems provide a higher degree of security and solutions that allow the on-line detection and localization of failures, as well as the switching of the control mode to a mode that allows us to continue the operation or safely stop the drive system. As the current sensors (CSs) are necessary to ensure precise control of the AC motors, in the event of their failure, one of two strategies can be used—hardware or software redundancy. The first strategy requires the use of additional measuring sensors. For this reason, the algorithmic solution, based on the Luenberger Observer (LO), has been proposed in this article as one of the software redundancy methods. In contrast to methods presented in the literature, the proposed solution allows one not only to compensate the stator current in a phase with a faulty CS, but also to adjust the correction of current estimation based on a measured signal in the other phase with a healthy CS. Extensive simulation studies in the direct rotor flux-oriented control (DRFOC) structure with the induction motor (IM) confirm the effectiveness of the proposed method. In addition, the proposed solution allows the drive system to be controlled even if all CSs are damaged.