Liquid crystal polymer networks (LCNs) have unique advantages as potential constituents of origami-based smart materials due to their reversible actuations and availability of fabrication techniques to create complex strain fields. Although identifying functional designs is crucial in making use of this technology, conventional approaches have largely consisted of trial-and-error experimentation. We introduce an inverse design procedure based on a topology optimization method to map out an LCN pattern with a desired spontaneous strain field to achieve prescribed shapes. In this study, we focus on a target deformation of a film to create an improved hinge to be integrated into an origami structure. Our preliminary results indicate the potential of using computational tools to determine what designs yield desired functionalities and how to best pattern LCN films to achieve them.