A major bottleneck in training end-to-end task-oriented dialog system is the lack of data. To utilize limited training data more efficiently, we propose Modular Supervision Network (MOSS), an encoder-decoder training framework that could incorporate supervision from various intermediate dialog system modules including natural language understanding, dialog state tracking, dialog policy learning and natural language generation. With only 60% of the training data, MOSS-all (i.e., MOSS with supervision from all four dialog modules) outperforms state-of-the-art models on CamRest676. Moreover, introducing modular supervision has even bigger benefits when the dialog task has a more complex dialog state and action space. With only 40% of the training data, MOSS-all outperforms the state-of-the-art model on a complex laptop network trouble shooting dataset, LaptopNetwork, that we introduced. LaptopNetwork consists of conversations between real customers and customer service agents in Chinese. Moreover, MOSS framework can accommodate dialogs that have supervision from different dialog modules at both framework level and model level. Therefore, MOSS is extremely flexible to update in real-world deployment.