The increasing abundance of data in the trajectories of personal movement opens up new opportunities for analyzing and mining human mobility. But the inherent personal information in the data raises the privacy concern. In this paper, the trajectories are not simply considered as a sequence of the coordinates in Euclidean space, they combine the semantics-aware information with the background knowledge of underlying map for the location points. A novel approach is then proposed to conceal the actually visited sensitive places. To this end, a cloaking region for each personalized sensitive place is built before a reasonable dummy trajectory in the cloaking region is constructed. The performance of our approach is evaluated based on a real-world trajectories dataset. And the results show that the proposed approach outperforms the existing privacy-preserving approaches.