The direct matrix converter is an AC-AC converter with no intermediate DC link. However, like the traditional indirect matrix converter, the predicted performance of matrix converters drastically reduce when operating under unbalanced grid voltages. This paper proposes a fractional-order sliding-mode control to improve the output performance of matrix converters. First, the topology and mathematical model of the matrix converter are analyzed to obtain the output power with an unbalanced grid. The output compensation is designed according to the output power expressions. Secondly, combined with the control objective and the mathematical model of direct matrix converter, a fractional-order sliding-mode control applied to the unbalanced power grid is designed. The designed controller aims to achieve constant active power and input unity power factor. Then, combined with output compensation, the output active power has no pulsation, and the reactive power can track the reference signal. Finally, a corresponding simulation model is established in Matlab/Simulink and RT-LAB experimental platform to verify the effectiveness of the algorithm. The experimental results show that the control performance of the fractional-order sliding-mode control is superior to traditional PI control. This work is supported by the National Natural Science Foundation of China (No. 51777120).