This paper presents a fractional-order sliding mode control scheme based on an RBF neural network (RBFFOSMC) for a direct three matrix converter (DTMC) operating under unbalanced grid voltages. The RBF neural network (RBF NN) is designed to approximate a nonlinear fractional-order sliding mode controller. The proposed method aims to achieve constant active power whilst maintaining a near unity input power factor. First, an opportune reference current is accurately generated according to the reference power and the RBFFOSMC is designed in a dq reference frame to achieve a perfect tracking of the input current reference. An almost constant active power, free of low-frequency ripples, is then supplied from the grid after compensating for the output voltage. Simulation and experimental studies prove the feasibility and effectiveness of the proposed control method.