A traditional discrete network design problem (DNDP) always assumes transportation infrastructure projects to be one-time events and ignores travelers’ delays caused by construction work. In fact, infrastructure construction usually lasts for a long time, and the impact on traffic can be substantial. In this paper, we introduce time dimension into the traditional DNDP to explicitly consider the impact of road construction and adopt an overtime policy to add flexibility to construction duration. We address the problem of selecting road-widening projects in an urban network, determining the optimal link capacity, and designing the schedule of the selected projects simultaneously. A time-dependent DNDP (T-DNDP) model is developed with the objective of minimizing total weighted net user cost during the entire planning horizon. An active-set algorithm is applied to solve the model. A simple example network is first utilized to demonstrate the necessity of considering the construction process in T-DNDP and to illustrate the tradeoff between the construction impact and the benefit realized through capacity extension. We also solve the T-DNDP model with data from the Sioux Falls network, which contains 24 nodes, 76 links, and 528 origin-destination (O-D) pairs. Computational results for the problem are also presented.