A multi-modal traffic assignment model is proposed in this study. Auto, bus and railway transport system, and their interactions are simultaneously expressed in the model. A model that determines optimal amount of antifreezing admixture dispersion is also proposed. This problem is formulated as Network Design Problem (NDP) because passengers would change both transport modes and routes depending on the level of service for road network determined by the amount of antifreezing admixture dispersed in winter. Responses from passengers to the amount of antifreezing admixture dispersed are expressed by the multi-modal traffic assignment model. Lastly, calculation results obtained by using test network are presented.