Vehicle-to-grid (V2G) networks, as an emerging smart grid paradigm, can be integrated with renewable energy resources to provide power services and manage electricity demands. When accessing electricity services, an electric vehicle (epsilon V) typically provides authentication or/and payment information containing identifying data to a service provider, which raises privacy concerns as malicious entities might trace epsilon V activity or exploit personal information. Although numerous anonymous authentication and payment schemes have been presented for V2G networks, no such privacy-preserving scheme supports authentication and payment simultaneously. Therefore, this paper is the first to present a privacy-preserving authentication scheme with anonymous payment for V2G networks (PAP, for short). In addition, this scheme also supports accountability and revocability, which are practical features to prevent malicious behavior; minimal attribute disclosure, which maximizes the privacy of epsilon V when responding to the service provider's flexible access policies; payment binding, which guarantees the accountability in the payment phase; user-controlled linkability, which enables epsilon V to decide whether different authentication sessions are linkable for continuous services. On the performance side, we implement PAP with the pairing cryptography library, then evaluate it on different hardware platforms, showing that it is essential for V2G applications.