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In this study, we created a practical traffic assignment model for a multimodal transport system considering low-mobility groups with the aim of providing the foundation of transportation network design for low-mobility individuals. First, the route choice equilibrium for walking, non-vehicle, and private car modes is described using the logit function, which is formulated as a variational inequality problem considering different low-mobility groups. Then, the practicalities related to travel times at intersections, traffic barricades between different lanes, and fuel fees of private cars are integrated to design a generalized travel cost function. Last, the method of successive weight averages is used to solve the proposed model. The model and its solution are verified based on a real case study of the city of Wenling in China. The sensitivity of adjustment parameters related to travel costs are analyzed, the practicality of the proposed model is explored, and the results of traffic assignment for different low-mobility groups are discussed.