As an important component of task-oriented dialogue systems, dialogue state tracking is designed to track the dialogue state through the conversations between users and systems. Multi-domain dialogue state tracking is a challenging task, in which the correlation among different domains and slots needs to consider. Recently, slot self-attention is proposed to provide a data-driven manner to handle it. However, a full-support slot self-attention may involve redundant information interchange. In this paper, we propose a top-k attention-based slot self-attention for multi-domain dialogue state tracking. In the slot self-attention layers, we force each slot to involve information from the other k prominent slots and mask the rest out. The experimental results on two mainstream multi-domain task-oriented dialogue datasets, MultiWOZ 2.0 and MultiWOZ 2.4, present that our proposed approach is effective to improve the performance of multi-domain dialogue state tracking. We also find that the best result is obtained when each slot interchanges information with only a few slots.