In computer-aided design for moldings, automatic generation of parting curves is a crucial design task that has an influence on the entire mold structure. This article proposes a hybrid approach for determining the parting curves of free-form computer-aided design models. Based on the analysis of the geometric properties of specific entities and mathematical conditions, different sets of moldable surfaces for two-half molds and side cores are identified. All surfaces that do not contribute to the parting curves can be subtracted from these surface sets. The proposed parting curve is generated based on the combination of both the outermost boundary edges and the visible silhouette segments of the relevant surfaces. By the techniques of silhouette detecting, edge projecting, and ray testing, the proposed algorithm overcomes the problems found in conventional research that cannot guarantee that the outermost curves generated are the actual silhouette of a free-form surface. In addition, by eliminating all irrelevant surfaces and without using the surface approximation method, the proposed approach achieves the goals of obtaining high accuracy coupled with high performance. Two examples of industrial models are used to demonstrate the performance and robustness of the proposed algorithm. The approach is generic in nature, which allows it to be applied to any complex geometry in three-dimensional mold design.