The purpose of this paper is to introduce a new method for the design process of complex systems affected by epistemic uncertainty. In particular, a multi-layer network is proposed to model the whole design process and describe the transition between adjacent phases. Each layer represents a design phase with a particular detail definition, each node a subsystem and each link a sharing of information. The network is used to quantify and propagate uncertainty through the different layers (design phases) where, proceeding from phase A to phase F, the detail of the mathematical model is increased. Thus, it can be considered as a multi-fidelity approach for the design of a complex system affected by epistemic uncertainty. The framework of Dempster-Shafer Theory of Evidence (DST) is used to model epistemic uncertainty and the model is then called Multi-Layer Evidence Network Model (ML-ENM).