The success of current Entity Alignment (EA) task depends largely on the supervision information provided by labeled data. Considering the cost of labeled data, most supervised methods are difficult to apply in practical scenarios. Therefore, more and more works based on contrastive learning, active learning or other deep learning techniques have been developed, to solve the performance bottleneck caused by the lack of labeled data. However, the existing unsupervised EA methods still have some limitations, either their modeling complexity is high or they cannot balance the effectiveness and practicality of alignment. To overcome these issues, we propose a Simplifying and Learnable graph convolutional attention network for Unsupervised Knowledge Graphs alignment method (SLU). Specifically, we first introduce LCAT, a new and simple framework as the backbone network to model the graph structure of two KGs. Then we design a reconstruction method of relation structure based on potential matching relations for efficiently filtering invalid neighborhood information of aligned entities, to improve the usability and scalability of SLU. Impressively, a similarity function based on consistency is proposed to better measure the similarity of candidate entity pairs. Finally, we conduct extensive experiments on three datasets of different sizes (15K and 100K) and different types (cross-lingual and monolingual) to verify the superiority of SLU. Experimental results show that SLU significantly improves alignment accuracy, outperforming 25 supervised or unsupervised methods, and improving 6.4% in Hits@1 over the best baseline in the best case.