This paper proposes a predictive voltage control strategy for a direct matrix converter used in a renewable energy distributed generation (DG) system. A direct matrix converter with LC filters is controlled in order to work as a stable voltage supply for loads. This is especially relevant for the stand-alone operation of a renewable DG where a stable sinusoidal voltage, with desired amplitude and frequency under various load conditions, is the main control objective. Model predictive control is employed to regulate the matrix converter so that it produces stable sinusoidal voltages for different loads. With predictive control, many other control objectives, e.g., input power factor, common-mode voltage and switching frequency, can be achieved depending on the application. To reduce the number of required measurements and sensors, this work utilizes observers and makes use of the switch matrices. In addition, the voltage transfer ratio can be improved with the proposed strategy. The controller is tested under various conditions including intermittent disturbance, non-linear loads and unbalanced loads. The proposed controller is effective, simple, and easy to implement. Simulation and experimental results verify the effectiveness of the proposed scheme and control strategy. This proposed scheme can be potentially used in microgrid applications.