This paper addresses (lie optimal disturbance attenuation problem by Output feedback for multivariable linear systems with delayed inputs. The attenuation is optimal in the sense that the controller minimizes the maximal amplitude of the plant output in response to Such a disturbance. The controller is a general feedback, involving an observer, a state predictor, and a predicted state feedback. The optimal disturbance attenuation problem is [formulated in terms of an equivalent system without delay. The optimal bound of the disturbance attenuation is then characterized, and it is shown that the optimal controller tends to have high gains. A necessary and Sufficient condition to guarantee the existence of an optimal solution is provided using the geometric approach.