The planning of bikeway networks in Taiwan is currently performed using a trial-and-error experience-based method, which is neither effective nor efficient. There is little in the literature on effective models and solution methods for solving the bikeway network-planning problem under a roadway network system. In this study, the authors employ network flow techniques and a mathematical programming method to consider demand value, travel time, and safety restrictions in developing a planning model for a preliminary commuter-bikeway network under a roadway network system. To efficiently solve large-scale real-world problems, authors develop a solution algorithm for each model based on Lagrangian relaxation methods. To evaluate the proposed model and algorithm, authors randomly generate various large problem scenarios under the real parameters of Taipei city, performing case studies. The results show that the model and algorithm could be useful. Finally, authors offer conclusions and suggestions for future research.