The data form of trajectory by introducing time and spatial dimension totally differs from traditional static data and has greatly enriched the content of data itself. Clustering spatio-temporal trajectory can find the motion and behavior patterns of moving object as it evolves over time. Generally, an object moves along a straight line at certain speed till it changes its direction and/or speed. However, the motion way, special semantics and fuzziness in trajectory data has not completely been taken yet into account during the clustering process. In this paper, we study the semantic extension of trajectory model, similarity measure and fuzzy trajectory clustering algorithm based on data reduction. First, a coarse-grained measure function of similarity based on data reduction, which includes location similarity, motion direction and speed similarity, is defined. Second, we propose a new fuzzy clustering algorithm named TraFCM for spatio-temporal trajectory data based on the defined similarity measure which can enhance the computing efficiency observably. The evaluation of experiment performed on synthetic and real trajectory indicate the effectiveness and efficiency of our approach. And the new clustering method shows excellent performance even if trajectories data are reduced to a half of raw data.