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Rapid development of mobile devices makes it possible that billions of mobile and personal devices will soon be used in every daily routine work. This emerging environment presents a number of challenging problems in several research areas including databases. The need for managing and querying continuously moving objects is among the new demands of this development. Although global positioning systems (GPS) are widely used nowadays, it is still a fact that the position information obtained is not accurate at every time instant. Thus, in most cases trajectory information is in fact "expected" trajectory with uncertainty. An interesting problem is indexing and querying trajectories with uncertain information. In this paper we introduce a data model for moving object trajectories with uncertainty and develop a new index structure (TPRU-tree) for uncertain trajectories based on TPR-tree. We discuss query evaluation using TPRU-tree and present an empirical study.