Several algorithms have been proposed for discovering patterns from trajectories of moving objects, but only a few have concentrated on outlier detection. Existing approaches, in general, discover spatial outliers, and do not provide any further analysis of the patterns. In this paper we introduce semantic spatial and spatio-temporal outliers and propose a new algorithm for trajectory outlier detection. Semantic outliers are computed between regions of interest, where objects have similar movement intention, and there exist standard paths which connect the regions. We show with experiments on real data that the method finds semantic outliers from trajectory data that are not discovered by similar approaches.