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The ubiquity of location-aware mobile devices and information systems has made it possible to collect large amounts of movement data such as trajectories of moving objects. However, it must be carefully managed to ensure that the privacy of each moving object or sensitive location is guaranteed. In this paper, we investigate how different locations of a geographical map can meet their individual privacy protection requirements using differential privacy (DP). More specifically, we aim to guarantee that the inclusion of any trajectory data record in a trajectory database does not substantially increase the risk to its privacy, while ensuring the required level of privacy protection for each location. To achieve this, we introduce the concept of personalized-location differential privacy (PLDP) for trajectory databases, and devise a differentially private algorithm, called PLDP-TD, that implements this new concept. PLDP-TD …