Owing to the advances of computer and communication technologies, clustering analysis on moving objects has attracted increasing attention in recent years. An interesting problem is to find the moving clusters composed of objects which move along for a sufficiently long period of time. However, a moving cluster inclines to break after some time because of the goal change in each individual object. In order to identify the set of moving clusters, we propose the formal definition of moving clusters with semantically clear parameters. Based on the definition, we propose delicate approaches to cluster moving objects. The proposed approaches are evaluated using data generated with and without underlying model. We validate our approaches with a through experimental evaluation and comparison.