To eliminate the common-mode voltage (CMV) for matrix converters, this paper proposes a current sensorless model predictive control with reduced calculation overhead. In contrast to other traditional CMV-reducing methods which use all permissible switching configurations, this method synthesizes the output voltage and the input current with only six rotating vectors that lead to zero CMV. The proposed technique does not need to predict future load currents and source currents for those six rotating vectors, which provides another advantage in term of computation efficiency. Additionally, all current sensors are removed by using a Luenberger state observer instead in the control loop for cost reduction. The effectiveness of the proposed method is evaluated through simulation in different operation conditions.