A service-based system (SBS) defined with minimum and maximum execution time can be easily transferred into a temporal structured workflow. The analysis technique on a temporal structured workflow can thus be applied on SBS. In the past, there were several researches working on artifact anomaly detection in a workflow. Their results are useful and have been published. However, their works does not consider temporal factor and the anomalies detected may not exist in a real system. In other word, they are less effective in a temporal structural workflow (TS workflow). Neither for SBS. Besides, the time complexity of these methods are NP, not efficient either. In this paper, we re-define the anomalous behaviors and develop an approach to discover artifact anomalies in a TS workflow. In the approach, we design several algorithms to detect the anomalies defined. By using our approach, workflow and SBS designers can detect artifact anomalies more precisely inside their TS workflow and thus might prevent run-time errors more effectively.