Based on Lyapunov theorem and sliding mode control scheme, the chaos control of fractional memristor chaotic time-delay system was studied. In order to stabilize the system, a fractional sliding mode control method for fractional time-delay system was proposed. In addition, Lyapunov stability theorem was used to analyze the control scheme theoretically, which guaranteed the stability of commensurate and non-commensurate order systems with or without uncertainties and disturbances. Furthermore, to illustrate the feasibility of controller, the conditions for designing the controller parameters were derived. Finally, the simulation results presented the effectiveness of the designed strategy.