High utility itemsets (HUIs) mining refers to discovering sets of items that not only co-occur but also carry high utilities (e.g., high profits). HUI mining receives extensive attentions in recent years due to the wide applications in various domains like commerce and biomedicine. However, huge number of HUIs might be produced to users, which degrades the efficiency of the mining process. A promising solution to this problem is to mine closed+ high utility itemset (CHUI), a compact and lossless representation of HUIs. Nevertheless, existing algorithms incur the problem of producing a large amount of candidates, which degrades the mining performance in terms of time and space. In this paper, a novel algorithm named CHUI-Miner (Closed+ High Utility Itemset mining without candidates) for mining CHUIs is proposed, which directly computes the utility of itemsets without producing candidates. To our best knowledge, this is the first work addressing the issue of mining CHUIs without candidate generation. Experimental results show that CHUI-Miner is several orders of magnitude faster than the state-of-the-art algorithms.