We consider the problem of secure delivery in a single-hop caching network with a central server connected to multiple end-users via an insecure multi-cast link. The server has a database of a set of files (content) and each user, which is equipped with a local cache memory, requests access one of the files. In addition to delivering users' requests, the server needs to keep the files (information-theoretically) secure from an external eavesdropper observing the underlying communications between the server and users. We focus on an important class of content placement strategies where the pre-fetching is required to be uncoded and caches are filled with uncoded fragments of files. In this paper, we establish the exact characterization of secure rate-memory trade-off for the worst-case communication rate through a matching converse under the constraint of uncoded cache placement where the number of users is no larger than the number of files in the database.