Fraud transactions obtain the rights and interests of e-commerce platforms by illegal ways, and have been the emerging threats to the healthy development of these platforms. Recently, user behavioral data is extensively exploited to detect fraud transactions, and it is usually processed as a sequence consisting of individual actions. However, such sequence-like user behaviors have logical patterns associated with user intentions, which motivates a fine-grained management strategy that binds and cuts off these actions into intention-related segments. In this paper, we devise a tree-like structure named behavior tree to reorganize the user behavioral data, in which a group of successive sequential actions denoting a specific user intention are represented as a branch on the tree. We then propose a novel neural method coined LIC Tree-LSTM(Local Intention Calibrated Tree-LSTM) to utilize the behavior tree for fraud transactions detection. In our LIC Tree-LSTM, the global user intention is captured by an attentional method applied on different branches. Then, we calibrate the entire tree by attentions within tree branches to pinpoint the balance between global and local user intentions. We investigate the effectiveness of LIC Tree-LSTM on a real-world dataset of Alibaba platform, and the experimental results show that our proposed algorithm outperforms state-of-the-art methods in both offline and online modes. Furthermore, our model provides good interpretability which helps us better understand user behaviors.