In this paper, the Smith predictor, known as the dead-time compensator, is extended to the control of a class of nonminimum phase processes referred to as inverse-response processes. An analytical design procedure is developed based on modern H-infinity control theory. The resulting controller can provide not only the suboptimal frequency domain performance but also the quantitative time domain specifications for step response. The performance and robustness of the closed-loop system are discussed. For illustration, numerical examples are given to compare the proposed controller to those previous.