In this paper, a new modulation strategy to control the 3×3 Matrix Converter (MC) under unbalanced input voltage conditions is proposed. The proposed strategy ensures that optimal performance of the MC is achieved over the entire range of operation, including the case when the converter operates with an output voltage greater than maximum attainable balanced output voltage under unbalance input voltage conditions. The implementation of the modulation strategy involves selection of the most appropriate switching states and calculation of the corresponding duty cycles to ensure that error in the output voltage and the input current is minimized. Performance of the proposed strategy is evaluated based on time-domain simulation studies in the MATLAB/Simulink software environment and experimentation on a scaled-down laboratory prototype.