This paper investigates the robust H∞ faulttolerant controller design under actuator failure for a class of the stochastic Markov jump timedelay systems with parameter uncertainties. The existence condition of the state feedback robust H∞ faulttolerant controller with actuator failure is presented. The robust H∞ faulttolerant control algorithm is derived in the form of linear matrix inequality via the Lyapunov stability theory. The proposed control does not need to estimate the boundary value of an actuator fault, nor does it depend on fault detection and diagnostic devices. By solving the linear matrix inequality, a robust faulttolerant controller, which makes the closedloop system asymptotically stable and whose H∞ performance is restricted by a given bound, is designed such that its structure is comparably simpler and does not require a large number of calculations. The designed controller is applied to a UAV illustrative example. The numerical results and computer simulation demonstrate the effectiveness of the proposed fault tolerant control.