High average-utility itemset mining (HAUIM) is an extension of high-utility itemset mining (HUIM), which provides a reliable measure to reveal utility patterns by considering the length of the mined pattern. Some research has been conducted to improve the efficiency of mining by designing a variety of pruning strategies and effective frameworks, but few works have focused on the maintenance algorithms in the dynamic environment. Unfortunately, most existing works of HAUIM still have to rescan databases multiple times when it is necessary. In this paper, the pre-large concept is used to update the discovered HAUIs in the newly inserted transactions and reduce the time of the rescanning process. To further improve the performance of the developed algorithm, two new upper-bounds are also proposed to decrease the number of candidates for HAUIM. Experiments were performed to compare the previous Apriori-like method and the proposed APHAUP algorithm with the two new upper-bounds in terms of the number of maintenance patterns and runtime in several datasets. The experimental results show that the proposed APHAUP algorithm has excellent performance and good potential to be applied in real applications.