Maximum torque per amper (MTPA) control can realize the minimum copper loss control of induction motor, which is often applied below the rated speed. In this paper, MTPA control is firstly extended from the constant torque mode to the constant apparent power mode and the constant voltage mode, and realizes MTPA control of induction motor in the whole speed range. Firstly, this paper establishes a MTPA-based nonlinear optimization problem in the whole speed range. Then, this optimization problem is analyzed and the analytical expressions are obtained for three different modes. Finally, finite control set-model predictive current control is adopted in this paper to achieve the fast stator current tracking. In the experimental part, the proposed algorithm is compared with the classical control strategy in this paper. The experimental results show that for the light load, the proposed algorithm reduces the stator current magnitude and improves the efficiency of induction machines.