With the rapid development of e-commerce and express industry, the air cargo network has become an important infrastructure. How to ensure the network robustness is of great importance for its operational safety. However, few robustness researches considered the attack cost. Furthermore, the traditional degree indexes are disabled to represent the node importance comprehensively. To solve these problems, considering the topological structure, industry characteristics, and the directionality of the air cargo network simultaneously, we propose a novel node importance evaluation method based on the TOPSIS method to better measure the attack cost. Then, an optimal attack strategy model considering attack cost constraints is proposed to achieve better effects. In order to verify the effectiveness of the proposed method, a real case study of China's air cargo network in 2017 is carried out. The results show that the proposed node importance index can better represent the node importance than the traditional degree indexes. Besides, the optimal attack strategy will change according to different attack budgets and the importance which defenders attach to the critical nodes, and the proposed optimal attack strategy model can achieve a higher attack effect than other strategies.