In this paper, a new scheme for sensorless speed control of multi-phase induction machine under unbalanced supply conditions is proposed. There are many methods that use speed and flux estimators for sensorless control of induction machines, but the proposed scheme is based on current estimation without flux and speed estimation, in which the stator controlled voltages are applied to the machine so that the difference between the estimated stator currents and the real currents of the machine are forced to decay to zero. The simulation results in MATLAB/Simulink show that the speed of the induction machine in the start-up and speed reversal test follows the reference speed well. Also, in the load rejection test, by applying a mechanical load on the machine and then removing it, the proposed control method has the ability to control the speed of the machine well, and the performance of the machine will be stable under these conditions. Finally, a sensitivity analysis to the changes in the machine parameters shows that the proposed method has a relatively acceptable performance.