In order to construct or extend entity-centric and event-centric knowledge graphs (KG and EKG), the information extraction (IE) annotation toolkit is essential. However, existing IE toolkits have several non-trivial problems, such as not supporting multi-tasks, and not supporting automatic updates. In this work, we present CollabKG, a learnable human-machine-cooperative IE toolkit for KG and EKG construction. Specifically, for the multi-task issue, CollabKG unifies different IE subtasks, including named entity recognition (NER), entity-relation triple extraction (RE), and event extraction (EE), and supports both KG and EKG. Then, combining advanced prompting-based IE technology, the human-machine-cooperation mechanism with Large Language Models (LLMs) as the assistant machine is presented which can provide a lower cost as well as a higher performance. Lastly, owing to the two-way interaction between the human and machine, CollabKG with learning ability allows self-renewal. Besides, CollabKG has several appealing features (e.g., customization, training-free, and label propagation) that make the system powerful and high-productivity. We holistically compare our toolkit with other existing tools on these features. Human evaluation quantitatively illustrates that CollabKG significantly improves annotation quality, efficiency, and stability simultaneously.