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Popular Transformer networks have been successfully applied to remote sensing (RS) image change detection (CD) identifications and achieve better results than most convolutional neural networks (CNNs), but they still suffer from two main problems. First, the computational complexity of the Transformer grows quadratically with the increase of image spatial resolution, which is unfavorable to very high-resolution (VHR) RS images. Second, these popular Transformer networks tend to ignore the importance of fine-grained features, which results in poor edge integrity and internal tightness for largely changed objects and leads to the loss of small changed objects. To address the above issues, this Letter proposes a Lightweight Structure-aware Transformer (LSAT) network for RS image CD. The proposed LSAT has two advantages. First, a Cross-dimension Interactive Self-attention (CISA) module with linear complexity is designed to replace the vanilla self-attention in visual Transformer, which effectively reduces the computational complexity while improving the feature representation ability of the proposed LSAT. Second, a Structure-aware Enhancement Module (SAEM) is designed to enhance difference features and edge detail information, which can achieve double enhancement by difference refinement and detail aggregation so as to obtain fine-grained features of bi-temporal RS images. Experimental results show that the proposed LSAT achieves significant improvement in detection accuracy and offers a better tradeoff between accuracy and computational costs than most state-of-the-art CD methods for VHR RS images.