Moving toward sustainable transportation is one of the essential issues in cities. Bicycles, as active transportation, are considered an important part of sustainable transportation. However, cyclists engage in more physical activity and air intake, making the quality of air that they inhale important in the programs that aim to improve the share of this mode. This paper develops a multi-modal transportation network design problem (MMNDP) to select links and routes for cycling, cars, and buses to decrease the exposure of cyclists to traffic-generated air pollution. The objective functions of the model include demand coverage, travel time, and exposure. The study also examined the effect of having exclusive lanes for bicycles and buses on the network. In the present study, the non-dominated storing genetic algorithm (NSGA-II) solves the upper-level and a method of successive average (MSA) unravels the lower level of the model. A numerical example and four scenarios evaluate the trade-off between different objective functions of the proposed model. The results reveal that considering exposure to air pollution in our model results in a slight increase in travel time (4%) while the exposure to traffic-generated air pollution for cyclists was reduced significantly (47%). Exclusive lanes also result in exposure reduction in the network (60%). In addition, the demand coverage objective function performs well in increasing the total demand in the network by 47%. However, more demand coverage leads to a rise in travel time by 28% and exposure by 58%. The model also showed an acceptable result in terms of exposure to traffic-generated air pollution compared to the model in the literature.