A data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. The continuous characteristic of streaming data necessitates the use of algorithms that require only one scan over the stream for knowledge discovery. Data mining over data streams should support the flexible trade-off between processing time and mining accuracy. In many application areas, mining frequent itemsets has been suggested to find important frequent itemsets by considering the weight of itemsets. In this paper, we present an efficient algorithm WSFI (Weighted Support Frequent Itemsets)-Mine with normalized weight over data streams. Moreover, we propose a novel tree structure, called the Weighted Support FP-Tree (WSFP-Tree), that stores compressed crucial information about frequent itemsets. Empirical results show that our algorithm outperforms comparative algorithms under the windowed streaming model.