In this paper, a method for mining frequent weighed closed itemsets (FWCIs) from weighted item transaction databases is proposed. The motivation for FWCIs is that frequent weighted itemset mining, as frequent itemset (FI) mining, typically results in a substantial number of rules, which hinders simple interpretation or comprehension. Furthermore, in many applications, the generated rule set often contains many redundant rules. The inspiration for FWCIs is that one potential solution to the rule interpretation problem is to adopt frequent closed itemset. This study first proposes two theorems and a corollary. One theorem is used for checking non-closed itemsets while joining two itemsets to create a new itemset and the other theorem is used for checking whether a new itemset is non-closed itemset or not. The corollary is used for checking non-closed itemsets when using Diffsets. Based on these theorems and corollary, an algorithm for mining FWCIs is proposed. A Diffset-based strategy for the efficient computation of the weighted supports of itemsets is described. A complete evaluation of the proposed algorithm is presented.