Abstract: The relationship between the similitude of data and the norm of a vector was discussed according to the definition of the similitude between multi-dimension data. A norm-based fuzzy clustering method for multi-dimension data was proposed. Each multi-dimension datum is regarded as a multi-dimension vector, and the data are sorted according to the vector-related norms. The approximate solution of clustering is presented. Each approximate cluster is further decomposed according to another norm by the same way. Then, the approximate solution of fuzzy clustering for multi-dimension data can be obtained. Finally, the exact clusters can be found from the approximate clusters using traditional methods. The fuzzy similarity relation does not need to be built when approximately clustering for multi-dimension data, so the total counts of accessing database is comparatively small. Hence, the method proposed is high efficient and fits to the clustering of large databases.