This paper describes a simplified capacitor voltage balancing scheme for a modular matrix converter operating in two-level switching mode. The proposed scheme is based on the conventional space vector modulation technique. By using two additional space vectors having opposite direction, the proposed controller is able to regulate all nine capacitor voltages in the converter. A Lyapunov-based control algorithm guarantees stability. This paper also includes experimental waveforms and data to verify the proposed control scheme. The control scheme can be implemented for a real time control using a microprocessor and FPGAs.