A new modulation and control strategy for a matrix converter induction motor drive is presented in this paper. A discrete model of the converter, motor and input filter is used to predict the behaviour of torque, flux and input power of the system. The switching state that optimizes the value of a quality function is selected. The predictive control method, referred to as predictive torque control for matrix converters is introduced in this paper, including a strategy to control the input power factor. One of the fundamental differences that the proposed approach presents is that it considers all valid voltage vectors generated by a matrix converter, including rotating vectors that are neglected by most control strategies.