The increasing availability of motion data creates unprecedent opportunities to change the paradigm for characterizing movement patterns. While cluster analysis is usually a useful starting point for understanding and exploring data, conventional clustering algorithms are not designed for handling trajectory data. Therefore, in this paper, we propose a direction-based clustering (DEN) method, which aims to group trajectories by moving directions. A key development challenge is how to transform direction information into a data format which is appropriate for traditional clustering algorithms to explore. To this end, we partition the space into grids and turn the movement statistics in a grid into a vector which represents the probabilities of moving directions within the grid. With such data transformation, we are able to develop a grid-level K-means clustering method for direction clustering. We illustrate the use of DEN for showing movement patterns and detecting outliers on real-world data sets.