Because of the importance of military expenditure to the security of nation, it has been a crucial and hot point in military research for decades. In the paper, we develop co-movement network of international military expenditure with the empirical mode decomposition method and Granger causality test. The results demonstrate that the most influential nations on different time scales are similar despite that the short-term components are disturbed. As the time scale increases, the pattern tends to be more clarified that the nations with developed economy or powerful military force, e.g., UK and USA are the most influential countries in co-movement of military expenditure. our paper provides a novel network approach to study the co-movement military expenditure path among nations from short- and long-term time-scale, where affectees and influencers are distinctive.