In this study, to explore the co-opetition (competition–cooperation) relationship between urban subway lines, we constructed three directed weighted subway models of a competition network, cooperation network, and co-opetition network based on the Space R model of a complex network. Taking Wuhan, China, as the research area, we established a Wuhan subway co-opetition network and analyzed the network’s complex characteristics. Through the analysis, we found that the competition network, cooperation network, and co-opetition network are all scale-free networks that present the characteristics of a high-clustering and short-distance small-world network. The co-opetition relationship between subway lines was mostly of a conventional type (55.56%) and unrelated type (41.67%), with only cooperative-dominant types found among the conventional types. The co-opetition effect between lines in the long-term network increased from 7.616 to 15.17, and the relationship strength of the competition and cooperation between lines increased significantly. The competition effect deflection angle of all subway lines in the network was found to be smaller than the cooperation effect declination angle. Additionally, all lines had a significant role in cooperation within the network, and cooperation played a dominant role in the co-opetition relationship.