Air Traffic Flow Management (ATFM) is considered as an effective way to alleviate flight delays in air routes network, but the traversing time of airways are not perfectly known due to uncertain factors such as weather conditions, etc. In this paper, we develope a distributionally robust mixed integer programming model for the ATFM problem by minimizing the total cost of travelling airway segments and flight delays. By exploiting the moment information of the fuel consumption data, we construct the moment ambiguity set which contains the actual distribution of uncertainty. Meanwhile, we derive an equivalent reformulation and propose a cutting plane-based decomposition algorithm to solve the model. Furthermore, comparing to the robust model, we verity the effectiveness and robustness of the proposed model by presenting the computational results for the small-sized instances such as 2-airport network.