As the negative environmental impacts of transportation systems become more severe, governments and environmental groups are seeking more sustainable transportation options, such as replacing fuel-powered vehicles with electric vehicles and expanding public transportation systems to reduce the number of people driving on their own, in order to reduce the environmental impacts of transportation systems. At present, the rapid expansion of public transportation systems is not an easy task and requires a long period of time to plan for expansion and construction, so people are increasingly looking to find means of transportation that meet sustainable conditions as solutions. In this context, electric bicycles are one of the solutions that people can choose, with benefits such as energy saving, carbon reduction, effective air pollution reduction, and simple and labor-saving riding. However, in Taiwan, despite the many benefits of electric bicycles, their popularity is not high. Therefore, this study focuses on the factors that affect the purchase of electric bicycles in Taiwan. The Influential Network Relation Map (INRM) generated by the Z-based Decision-making Trial and Evaluation Laboratory (Z-DEMATEL) technique is used to describe the influence relationships among the factors and to establish the key evaluation criteria of electric bicycle purchase intention. The results indicate that vehicle price, safety, motor performance, battery life, and battery durability are the most important factors in purchasing electric bicycles. Furthermore, the power of motor is considered as the factor that most significantly affects other criteria, while safety and price are most likely to be affected by other criteria. This study has contributed to academia and industry, for the dependency weights of these factors are set to provide a scientific and systematic way to show how consumers think in the decision-making process and to provide more reliable information and management implications for the electric bicycle industry.