In this article, a trajectory-decomposition-based approach to output tracking with preview for nonminimum-phase systems is proposed. When there exists a finite (in time) preview of the future desired trajectory, precision output tracking of nonminimum-phase systems can be achieved by using the preview-based stable-inversion technique. The preview-based stable-inversion technique has been successfully implemented in various high-speed positioning applications. The performance of this approach, however, can become sensitive to system dynamics uncertainty. Moreover, the computation involved in the implementation of this approach can be demanding. In the proposed approach, such preview-based inversion related challenges are addressed by integrating the notion of signal decomposition and the iterative learning control technique together. Particularly, a library of desired output elements and their corresponding control input elements is constructed, and the ILC techniques such as the recently-developed model-less inversion-based iterative control (MIIC) are used to obtain the control input elements that achieve precision output tracking of the corresponding desired output elements. Then the previewed future desired trajectory is decomposed as a summation of desired output elements, and the control input is synthesized by using the input elements selected for the corresponding output elements with chosen pre-actuation time. Furthermore, the required pre-actuation time is quantified based on the stable-inversion theory. The proposed approach is illustrated through simulation study of a nanomanipulation application using a nonminimum-phase piezo actuator model.