Due to the absence of actual obligation description and implementation abilities in existing DRM (digital rights management) mechanism, this paper presents an obligation authorization model and its implementation framework that can be applied in DRM. The model is based on distributed temporal logic and Active-U-Datalog rules, which empowers the model to express event-driven, time-driven, obligation compensation and other semantics of obligation descriptions, and also give the model a favorable feasibility of implementation. The semantics and syntax of the model are analyzed and explained. And the implementation mechanism of the model is discussed. Finally, the implementation, application and expressiveness of the model are showed and illustrated. The model improves the flexibility and capability of usage control of data in DRM system.