A different approach to perform the control of an induction machine fed by a matrix converter (MC) is presented in this paper. The proposed technique is based on predictive control and effectively controls input and output variables to the power converter, as expected from an MC. The method allows the use of all valid switching states, including rotating vectors that are not considered in most control techniques, as space vector modulation or direct torque control for induction machines fed by MCs. Experimental results show the excellent performance of the proposed approach, with low-distortion input currents, adjustable power factor, sinusoidal output currents with smooth frequency transitions, and good speed control in motoring and regeneration conditions, even working under an unbalanced power supply. The implementation and comprehension of the method should be considered simple compared to other control strategies with similar features. The high computational effort required should not be a problem considering recent progresses in digital signal processors-and even less in years to come.