Road network models form the foundation of road network analyses, route planning, navigation and traffic predictions. However, existing models cannot effectively represent the dynamic topological relationships that exist among lanes due to the effects of time-dependent traffic control measures. To address this problem, we propose a time-dependent road network model (TRNM) to represent these topological relationships, and present its construction method based on a traditional carriageway network model. We constructed two TRNMs in Changzhou and Shanghai and then conducted path-planning experiments to verify the effectiveness of the models. Our results showed that TRNMs could be constructed readily from traditional road networks without introducing large volumes of data, while effectively representing the time-dependent topological relationships among lanes. It is particularly beneficial to path planning, as it not only provides valid and shorter paths but also lane-level navigation information. Time-dependent road network models mirror real-world road networks and can represent more time-dependent traffic controls, such as non-periodic changes at different frequencies. The TRNM developed here can provide support for applications based on road network models, as well as a useful reference for the geographic information system (GIS) and complex networks.