Mining a closed high-utility itemset is a prevalent research task in analyzing transaction databases. However, numerous target itemsets are generated in the closed high-utility itemset mining task. As a result, too many closed high-utility itemsets (CHUIs) will not only increase the time and memory consumption but also make it difficult for users to analyze the results. To address this problem, this paper proposes an efficient algorithm called FCHUIM, which is used to mine a concise representation called the frequent closed high-utility itemset (FCHUI). FCHUIM is based on a total summary list structure for storing and retrieving utility lists without repeatedly scanning the database. In addition, the proposed algorithm uses an effective upper bound on the utility of items to efficiently reduce the search space. Furthermore, a precheck method and a nested list structure are also introduced in this work to quickly discover FCHUIs. To test the performance of FCHUIM, we conduct extensive experiments on real-life and synthetic databases. We also select two state-of-the-art algorithms to compare with FCHUIM: CHUI-Miner and CLS-Miner. The results show that FCHUIM performs well on databases, whether the databases are dense or sparse.