EVs provide a promising green solution to reduce dependence on fossil fuel and the emission of greenhouse gas. This article concerns hybrid EV systems that contain both wired charging and wireless charging vehicles. To the best of our knowledge, we are the first to discuss how to jointly use these two types of charging methods whose advantages are complementary to each other; for example, wireless charging has better user friendliness and flexibility, while wired charging can provide higher charging efficiency and bidirectional energy transmission. We believe such a hybrid system can benefit us much more than either a pure wireless or pure wired EV charging system. On the other hand, we also pay attention to a practically important problem with DSM. The existing schemes can hardly ensure efficient and stable charging services in the foreseeable future due to the rapidly increasing number of electric vehicles and the limited capacity of local grids. To address this issue, we propose a software-defined green framework for hybrid EV charging networks, which consists of three planes: the application plane provides customized services for users; the control plane aims to guide both data flow and energy flow to implement an efficient and economic strategy for EV charging; and the physical plane collects the information from a large number of EVs and other infrastructures. Furthermore, we present a DSM approach for EV charging as a case study. Simulation results reveal that our proposals could achieve delightful DSM performance in the proposed software-defined EV charging networks. Although the proposed hybrid framework offers promising opportunities, we still face some technical challenges that solicit further research efforts from both academia and industry, which are discussed in detail at the end of this article.