Delta mechanism is one of the well-known parallel mechanisms used in robotic applications. In this study, the trajectory behavior of a novel Delta mechanism, which was designed and fabricated using layer-by-layer origami method, is investigated utilizing the finite element method (FEM). The mechanism was modeled with the dimensions of the actual fabricated mechanism. The mechanism consists of four different materials where properties of two materials are extracted experimentally via the tensile testing process. The accuracy of our model was compared to the finite element simulations and the results indicated that the mechanism follows the given trajectory within 0.05 normalized root-mean-square (RMS) error with respect to the kinematic model. The impact of the fabrication and instrumentation errors on the trajectory was further analyzed using FEM simulations and the contribution of each factor on the error was categorized. This validated numerical model can be used in the future to accurately simulate the mechanics of origami-inspired mechanisms and to design new mechanisms.