Because of usefulness and comprehensibility, fuzzy data mining has been extensively studied and is an emerging topic in recent years. Compared with utility-driven itemset mining technologies, fuzzy utility mining not only takes utilities (e.g., profits) into account, but also considers quantities of items in each transaction for discovering high fuzzy utility itemsets (HFUIs). Thus, fuzziness can be regard as a key criterion to select high-utility itemsets, while the exiting algorithms are not efficient enough. In this paper, an efficient one-phase algorithm named Fuzzy-driven Utility Itemset Miner (FUIM) is proposed to find out a complete set of HFUIs effectively. In addition, a novel compact data structure named fuzzy-list keeps the key information from quantitative transaction databases. Using fuzzy-list, FUIM can discover HFUIs from transaction databases efficiently and effectively. Both completeness and correctness of the FUIM algorithm are proved by five theorems. At last, substantial experiments test three terms (runtime cost, memory consumption, and scalability) to confirm that FUIM considerably outperforms the state-of-the-art algorithms.