A predictive control scheme for the indirect matrix converter including a method to mitigate the resonance effect of the input filter is presented. A discrete-time model of the converter, the input filter, and the load is used to predict the behavior of the instantaneous input reactive power and the output currents for each valid switching state. The control scheme selects the state that minimizes the value of a cost function in order to generate input currents with unity power factor and output currents with a low error with respect to a reference. The active damping method is based on a virtual harmonic resistor which damps the filter resonance. This paper shows experimental results to demonstrate that the proposed control method can generate good tracking of the output-current references, achieve unity input displacement power factor, and reduce the input-current distortion caused by the input filter resonance.