Argumentation plays an important role in promoting deep learning, fostering conceptual change and supporting problem solving. The new “learning by arguing” paradigm leads to new learning opportunities. However, due to the difficulties in modeling human cognition, there are few learning systems that can facilitate argumentation dialogues between systems and learners. Fuzzy Cognitive Map (FCM) is an effective tool in modeling human cognition. This paper proposes an FCM based argumentation model. Based on this model we design an argumentative software agent to facilitate argumentative learning. Provided with the domain knowledge and argumentation capability, the agent is able to simulate a peer learner and automatically conduct argumentative dialogues with learners. The argumentative agent can be applied in general school education as well as special domains like diabetes education and eHealth decision support.