The objective of this study is to propose a novel definition of equity from the perspective of link performance with energy consumption and incorporate equity into the transportation network design problem (NDP). First, we introduce an aggregated equity measure and present the theoretical framework for the equity considering link travel time and energy consumption along with free flow traffic conditions. We demonstrate that a Braess paradox situation exists with regards to the proposed equity measure. Second, we formulate a bi-level modelling framework for the Link-based Equitable NDP (LE-NDP). The model is a multiobjective optimization program, where the upper level aims to minimize the total system travel time and optimize equity levels with respect to both travel time and energy consumption. The lower level then represents the flow response under user equilibrium conditions. To quantify the performance loss incurred relative to the equity criterion, we formulate the function of the price of fairness within the LE-NDP. Third, to solve the LE-NDP model, we develop a tailored heuristic solution method, which simulates the interaction between planners and travellers. The solution approach uses an ε-constraint method to identify Pareto-efficient solutions, and constraint optimization formulations are presented to solve the resulting single-objective program. Finally, the efficacy of the model and the solution algorithm is validated via case studies on three traffic networks. The results demonstrate that the proposed modelling device is capable of achieving more balanced solutions when the equity metrics are accounted for, and the developed solution method is efficient as a reference method in practice. The results also show the trade-offs between travel time and link-based equity, and indicate that equity metrics in terms of different travel costs, i.e. travel time and energy consumption, are shown to be conflicting design objectives for certain scenarios.