This paper focuses on the problem of robust and relaible H_∞ control design for linear uncertain systems with time-varying norm-bounded parameter uncertainty in the state matrix and also with actuator failures among a prespecified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. A state feedback control design is presented that stabilizes the plant and guarantees an H_∞-norm bound constraint on attenuation of augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. Hence we extend the existing results on robust H_∞ control of linear uncertain systems to robust and reliable H_∞ controller design. Necessary conditions for the existence of contoller are also derived.