Low-dose computed tomography (LDCT) can effectively reduce the risk of radiation to patients and currently attracts increasing attention in the field of medical imaging. Dose reduction introduces more noise to CT images, resulting in degradation of image quality, therefore requiring specialised image denoising methods. Recent advancements have highlighted the widespread use of convolutional neural networks (CNNs) and Transformer models for LDCT image denoising. However, existing methods still face challenges due to complex patterns and intensity similarities between edge details and lesion regions. To overcome the above challenges, this paper proposed a Cross-scale Residual Attention-based Edge-guide Transformer (CRA-Eformer) for LDCT denoising. Specifically, in each converter block, edge enhancement features are utilised to capture contour information and refine texture in the LDCT image through transposed attention, which helps to preserve the original structure of the lesion. Moreover, a novel cross-scale residual feed-forward network is designed, which focuses on both spatial and channel information, combining the residual structure to learn the recognition patterns of different intensity lesion regions in order to improve the quality of image reconstruction by using multi-scale information. To validate the effectiveness of our method, extensive experiments were conducted on the AAPM-Mayo Clinic LDCT Grand Challenge dataset. The results show that CRA-Eformer can maximise the preservation of structural and edge details of fine lesions while being comparable to state-of-the-art denoising algorithms in terms of denoising performance.