In this paper, we show that counterfactual explanations of confidence scores help users better understand and better trust an AI model's prediction in human-subject studies. Showing confidence scores in human-agent interaction systems can help build trust between humans and AI systems. However, most existing research only used the confidence score as a form of communication, and we still lack ways to explain why the algorithm is confident. This paper also presents two methods for understanding model confidence using counterfactual explanation: (1) based on counterfactual examples; and (2) based on visualisation of the counterfactual space.