This paper presents a learning control strategy for nonlinear process systems having inverse response. Implemented in a generalized Smith predictor configuration, the proposed control scheme integrates a learning-type nonlinear controller and a statically equivalent, minimum-phase predictor. The incorporated minimum-phase predictor is used to compensate an undesired inverse response behavior, which therefore enables the nonlinear controller to learn to control the nonlinear, non-minimum phase processes adaptively by simply using an output-error based learning algorithm. The effectiveness and applicability of the proposed scheme are demonstrated through controlling a nonlinear Van de Vusse reactor in the presence of inverse response characteristics. Performance comparison of the proposed scheme with a previously reported nonlinear technique is performed extensively in this work. The simulation results show that the proposed learning control strategy appears to be an effective and promising approach to the direct control of non-minimum phase nonlinear processes.