A novel predictive current control strategy for a sparse matrix converter is presented. The sparse matrix converter is functionally-equivalent to the direct matrix converter but has a reduced number of switches. The predictive current control uses a model of the system to predict the future value of the load current and generates the reference voltage vector that minimizes a given cost function so that space vector modulation is achieved. The results show that the proposed controller for sparse matrix converters controls the load current very effectively and performs very well through simulation and experimental results.