In recent years, the mining research over data stream has been prominent as they can be applied in many alternative areas in the real worlds. In [20], a framework for mining frequent itemsets over a data stream is proposed by the use of weighted slide window model. Two algorithms of single pass (WSW) and the WSW-Imp (improving one) using weighted sliding model were proposed in there to solve the data stream problems. The disadvantage of these algorithms is that they have to seek all data stream many times and generate a large set of candidates. In this paper, we have proposed a process of mining frequent itemsets with weights over a data stream. Based on the downward closure property and FP-Growth method [8,9] an alternative algorithm called WSWFP-stream has been proposed. This algorithm is proved working more efficiently regarding to computing time and memory aspects.