Finding high-importance patterns in data is an emerging data mining task known as High-utility itemset mining (HUIM). Given a minimum utility threshold, a HUIM algorithm extracts all the high-utility itemsets (HUIs) whose utility values are not less than the threshold. This can reveal a wealth of useful information, but the precise needs of users are not well taken into account. In particular, users often want to focus on patterns that have some specific items rather than find all patterns. To overcome that difficulty, targeted mining has emerged, focusing on user preferences, but only preliminary work has been conducted. For example, the targeted high-utility itemset querying algorithm (TargetUM) was proposed, which uses a lexicographic tree to query itemsets containing a target pattern. However, selecting the minimum utility threshold is difficult when the user is not familiar with the processed database. As a solution, this paper formulates the task of targeted mining of the top-k high-utility itemsets and proposes an efficient algorithm called TMKU based on the TargetUM algorithm to discover the top-k target high-utility itemsets (top-k THUIs). At the same time, several pruning strategies are used to reduce memory consumption and execution time. Extensive experiments show that the proposed TMKU algorithm has good performance on real and synthetic datasets.