Analysing and mining trajectories pose new challenges for trajectory privacy. We are addressing privacy issue for offline (historical) trajectories which are generally published for research. A fundamental research question in trajectory privacy domain is of trajectory anonymisation. k-anonymity is used as a standard for privacy which ensures that every entity in the dataset is indistinguishable from (k - 1) other entities. The proposed work aims at anonymising trajectories based on graph split method. We have used technique of constructing trajectory graph to simulate spatial and temporal relations of trajectories, based on which trajectory k-anonymity sets are found through graph split. For the purpose, we have proposed a novel method that uses earth mover's distance as a metric to find trajectory k-anonymity sets in contrast to Euclidean distance. It is discovered through a series of experiments that the proposed method is outperforming in terms of low information loss and computation time. Copyright © 2017 Inderscience Enterprises Ltd.